<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <!-- saved from url=(0089)http://prima.franko.lviv.ua/faculty/mechmat/Departments/Topology/seminararchiv_ta17_18.html --> <HTML><HEAD><TITLE>Lviv seminar on Topological Algebra archivta_2017-2018</TITLE> <META content="text/html; charset=unicode" http-equiv=Content-Type> <META content="text/html; charset=iso-8859-1" http-equiv=??????????-???><!-- *************** DHTML Outline (begin) ***************** --> <STYLE type=text/css>LI.oItem { COLOR: #000000; CURSOR: text } LI.oParent { COLOR: #000088; CURSOR: hand } UL UL { DISPLAY: none } </STYLE> <SCRIPT language=Javascript> <!-- // Returns the closest parent tag with tagName containing // the src tag. If no such tag is found - null is returned. function checkParent( src, tagName ) { while ( src != null ) { if (src.tagName == tagName) return src; src = src.parentElement; } return null; } // Returns the first tag with tagName contained by // the src tag. If no such tag is found - null is returned. function checkContent( src, tagName ) { var pos = src.sourceIndex ; while ( src.contains( document.all[++pos] ) ) if ( document.all[pos].tagName == tagName ) return document.all[pos] ; return null ; } // Handle onClick event in the outline box function outlineAction() { var src = event.srcElement ; var item = checkParent( src, "LI" ) ; if ( parent != null ) { var content = checkContent( item, "UL" ) ; if ( content != null ) if ( content.style.display == "" ) content.style.display = "block" ; else content.style.display = "" ; } event.cancelBubble = true; } // --> </SCRIPT> </head> <body background="backgr_3.gif" bgcolor="#FFCC66" text="#660000" vlink="#990000" alink="#990066" link="#990000"leftmargin="10" rightmargin="0" topmargin="1" > <Table width="95%" border=0 align="center"> <tr> <td > <img src="emb_1.gif"> </td> <td align="center"> <b><font size="+2"><a href=http:./seminarta.html> Scientific Seminar</a></font> <font size="+1"><br>at Geometry and Topology Department of <br> Ivan Franko National University of Lviv <br> <A href="seminararchiv_ta16_17.html"><IMG src="left.gif"></A> </b><i>Archive for</i><b> <font size="+2">(2017/2018)</font> </b><i>academic year</i></b></font> <a href="seminarta.html"><img src="right.gif"></a> </td> <td align="center"> <p> <b> <font size="+1"> <hr> <hr> Topological <br> Algebra <hr> <hr> </font></b> </p> </tr> </table> <Table width="91%" border=0> <tr><td colspan=3 HEIGHT="3" BORDER="1" ALIGN="left" bgcolor="#000080" ></tr> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> September 14, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> All participants </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <P align=center> <IMG src="Vivat-Bardyla.jpg" width="1190" height="1694"border=2 name="img1"></P> <UL type="square"><LI class='oItem'> <font size="+1"> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> September 27, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> M. Khylynskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On the &lambda;-polycyclic estension of a monoid <UL type="square"><LI class='oItem'> <font size="+1"> <p> We introduce the &lambda;-polycyclic estension of a monoid and discuss its properties. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> October 4, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> M. Khylynskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On the &lambda;-polycyclic estension of a monoid, II <UL type="square"><LI class='oItem'> <font size="+1"> <p> We introduce the &lambda;-polycyclic estension of a monoid and discuss its algebraic properties. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> October 18, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> T. Mokrytskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> The monoid $\mathcal{IPF}(\mathbb{N}^n)$ of order isomorphisms of principal filters of a power of the positive integers </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Let $n$ be any positive integer and $\mathcal{IPF}(\mathbb{N}^n)$ be the semigroup of all order isomorphisms between principal filters of the $n$-th power of the set of positive integers $\mathbb{N}$ with the product order. We study algebraic properties of the semigroup $\mathcal{IPF}(\mathbb{N}^n)$. In particular, we show that $\mathcal{IPF}(\mathbb{N}^n)$ bisimple inverse semigroup, describe Green's relations on $\mathcal{IPF}(\mathbb{N}^n)$ and its maximal subgroups. We prove that every non-identity congruence $\mathfrak{C}$ on the semigroup $\mathcal{IPF}(\mathbb{N}^n)$ is group. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> October 25, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> T. Mokrytskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> The monoid $\mathcal{IPF}(\mathbb{N}^n)$ of order isomorphisms of principal filters of a power of the positive integers, II </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Let $n$ be any positive integer and $\mathcal{IPF}(\mathbb{N}^n)$ be the semigroup of all order isomorphisms between principal filters of the $n$-th power of the set of positive integers $\mathbb{N}$ with the product order. We study algebraic properties of the semigroup $\mathcal{IPF}(\mathbb{N}^n)$. In particular, we show that $\mathcal{IPF}(\mathbb{N}^n)$ bisimple inverse semigroup, describe Green's relations on $\mathcal{IPF}(\mathbb{N}^n)$ and its maximal subgroups. We prove that every non-identity congruence $\mathfrak{C}$ on the semigroup $\mathcal{IPF}(\mathbb{N}^n)$ is group. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> November 1, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> A. Ravsky </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> A few open problems from Mathematics StackExchange </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We shall discuss on open problem in Topological Algebra posed in <A href="http://math.stackexchange.com/">Mathematics StackExchange</A> and <A href="http://mathoverflow.net/">MathOverflow</A>. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> November 8, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> O. Sobol </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Syntactic semigroup problem for the semigroup reducts of affine near-semirings over Brandt semigroups </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We discuss on the resuls of the paper: [J. Kumar and K. V. Krishna, <i><A href="http://dx.doi.org/10.1142/S1793557116500212">Syntactic semigroup problem for the semigroup reducts of affine near-semirings over Brandt semigroups</A></i>, Asian-Eur. J. Math. <b>9</b>, No. 1 (2016) 1650021 (10 pages)]. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> November 15, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> O. Sobol </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> Syntactic semigroup problem for the semigroup reducts of affine near-semirings over Brandt semigroups, II </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We discuss on the resuls of the paper: [J. Kumar and K. V. Krishna, <i><A href="http://dx.doi.org/10.1142/S1793557116500212">Syntactic semigroup problem for the semigroup reducts of affine near-semirings over Brandt semigroups</A></i>, Asian-Eur. J. Math. <b>9</b>, No. 1 (2016) 1650021 (10 pages)]. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> November 22, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> O. Sobol </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> Syntactic semigroup problem for the semigroup reducts of affine near-semirings over Brandt semigroups, III </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We discuss on the resuls of the paper: [J. Kumar and K. V. Krishna, <i><A href="http://dx.doi.org/10.1142/S1793557116500212">Syntactic semigroup problem for the semigroup reducts of affine near-semirings over Brandt semigroups</A></i>, Asian-Eur. J. Math. <b>9</b>, No. 1 (2016) 1650021 (10 pages)]. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> November 29, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> O. Sobol </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> On some reuslts of J. Kumar and K. V. Krishna </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We give a survey on the resuls of the papers: [J. Kumar and K. V. Krishna, <i><A href="https://doi.org/10.1080/00927872.2013.833211">Affine Near-Semirings Over Brandt Semigroups</A></i>, Communications in Algebra <b>42</b>, No. 12 (2014) 5252-5169], [J. Kumar and K. V. Krishna, <i><A href="https://arxiv.org/abs/1311.0789">Rank Properties of Multiplicative Semigroup Reduct of Affine Near-Semirings over $B_n$</A></i>, arXiv:1311.0789v2], [J. Kumar and K. V. Krishna, <i><A href="https://arxiv.org/abs/1308.4087">The Ranks of the Additive Semigroup Reduct of Affine Near-Semiring over Brandt Semigroup</A></i>, arXiv:1308.4087v1], [J. Kumar and K. V. Krishna, <i><A href="http://dx.doi.org/10.1142/S1793557116500212">Syntactic semigroup problem for the semigroup reducts of affine near-semirings over Brandt semigroups</A></i>, Asian-Eur. J. Math. <b>9</b>, No. 1 (2016) 1650021 (10 pages)], [J. Kumar and K. V. Krishna, <i><A href="https://link.springer.com/chapter/10.1007/978-81-322-2488-4_10">Radicals and Ideals of Affine Near-Semirings Over Brandt Semigroups</A></i>, Romeo P., Meakin J., Rajan A. (eds), Semigroups, Algebras and Operator Theory. Springer Proceedings in Mathematics & Statistics, vol 142. Springer, New Delhi, pp 123-133] and [J. Kumar and K. V. Krishna, <i><A href="https://link.springer.com/article/10.1007/s00233-016-9826-5">Rank properties of the semigroup reducts of affine near-semirings over Brandt semigroups</A></i>, Semigroup Forum <b>93</b>, No. 3 (2014) 516-534]. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> December 6, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> On topological semilattices with compact maximal chains </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We investigate topological semilattices with compact maximal chains. In particular, we prove that a topological semilattice X is multiclosed in the class of topological semigroups iff X is a semilattice with compact maximal chains. Some open problems will be posed. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> December 13, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> On topological semilattices with compact maximal chains, II </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We investigate topological semilattices with compact maximal chains. In particular, we prove that a topological semilattice X is multiclosed in the class of topological semigroups iff X is a semilattice with compact maximal chains. Some open problems will be posed. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> December 19, 2017 </font><td valign="top" width="15%" > <b><font size="+2"> All participants </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <P align=center> <IMG src="Vivat-Pozdniakova.jpg" width="1190" height="1694"border=2 name="img1"></P> <UL type="square"><LI class='oItem'> <font size="+1"> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> January 3, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> On topological semilattices with compact maximal chains, III </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We investigate topological semilattices with compact maximal chains. In particular, we prove that a topological semilattice X is multiclosed in the class of topological semigroups iff X is a semilattice with compact maximal chains. Some open problems will be posed. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> January 24, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> A. Ravsky </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> <b> Two new algebra working problems, II </b> </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Inspired by questions from Mathematics StackExchange (<A href="http://math.stackexchange.com/">http://math.stackexchange.com/</A>), the speaker will pose two new algebra working problems for investigation for the participants of the seminar. One (<A href="https://math.stackexchange.com/questions/2575974/venn-diagram-with-rectangles-how-many-among-binomnk-regions-created-by-i">http:https://math.stackexchange.com/questions/2575974/venn-diagram-with-rectangles-how-many-among-binomnk-regions-created-by-i</A>) has deep roots in computer science and graph drawing formulation, but the speaker will ask about some properties of the semilattice $(\mathbb N^2,\min)$, the other (<A href="https://math.stackexchange.com/questions/2363770/having-a-graph-of-complaints-with-10-of-enemies-prove-that-you-always-may-arre">https://math.stackexchange.com/questions/2363770/having-a-graph-of-complaints-with-10-of-enemies-prove-that-you-always-may-arre</A>) is devoted to finite oriented graphs with out-degree one, that is a monounary algebras and will be proposed for Inna Pozdniakova. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> February 14, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> O. Sobol,<br> <A href="./Gutik_mine.html">O. Gutik</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> On feebly compact semitopological semilattice $\exp_n\lambda$ </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We discuss on feebly compact shift-continous topologies $\tau$ on the semilattice $\left(\exp_n\lambda,\cap\right)$. It is proved that for any shift-continuous $T_1$-topology $\tau$ on $\exp_n\lambda$ the following conditions are equivalent: $(i)$ $\tau$ is countably pracompact; $(ii)$ $\tau$ is feebly compact; $(iii)$ $\tau$ is $d$-feebly compact; $(iv)$~$\left(\exp_n\lambda,\tau\right)$ is an $H$-closed space; $(v)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially countably pracompact; $(vi)$~$\left(\exp_n\lambda,\tau\right)$ is selectively sequentially feebly compact; $(vii)$~$\left(\exp_n\lambda,\tau\right)$ is selectively feebly compact; $(viii)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially feebly compact; $(ix)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathfrak{D}(\omega)$-compact; $(x)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathbb{R}$-compact; $(xi)$~$\left(\exp_n\lambda,\tau\right)$ is infra H-closed. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> February 21, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> O. Sobol,<br> <A href="./Gutik_mine.html">O. Gutik</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> On feebly compact semitopological semilattice $\exp_n\lambda$, II </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We discuss on feebly compact shift-continous topologies $\tau$ on the semilattice $\left(\exp_n\lambda,\cap\right)$. It is proved that for any shift-continuous $T_1$-topology $\tau$ on $\exp_n\lambda$ the following conditions are equivalent: $(i)$ $\tau$ is countably pracompact; $(ii)$ $\tau$ is feebly compact; $(iii)$ $\tau$ is $d$-feebly compact; $(iv)$~$\left(\exp_n\lambda,\tau\right)$ is an $H$-closed space; $(v)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially countably pracompact; $(vi)$~$\left(\exp_n\lambda,\tau\right)$ is selectively sequentially feebly compact; $(vii)$~$\left(\exp_n\lambda,\tau\right)$ is selectively feebly compact; $(viii)$~$\left(\exp_n\lambda,\tau\right)$ is sequentially feebly compact; $(ix)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathfrak{D}(\omega)$-compact; $(x)$~$\left(\exp_n\lambda,\tau\right)$ is $\mathbb{R}$-compact; $(xi)$~$\left(\exp_n\lambda,\tau\right)$ is infra H-closed. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> March 14, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> A. Savchuk,<br> <A href="./Gutik_mine.html">O. Gutik</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> The semigroup of partial co-finite isometries of positive integers </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> The semigroup $\mathbf{I}\mathbb{N}_{\infty}$ of all partial co-finite isometries of positive integers is discussed. We describe the Green relations on the semigroup $\mathbf{I}\mathbb{N}_{\infty}$, its band and proved that $\mathbf{I}\mathbb{N}_{\infty}$ is a simple $E$-unitary $F$-inverse semigroup. It is described the least group congruence $\mathfrak{C}_{\mathbf{mg}}$ on $\mathbf{I}\mathbb{N}_{\infty}$ and proved that the quotient-semigroup $\mathbf{I}\mathbb{N}_{\infty}/\mathfrak{C}_{\mathbf{mg}}$ is isomorphic to the additive group of integers $\mathbb{Z}(+)$. An example of a non-group congruence on the semigroup $\mathbf{I}\mathbb{N}_{\infty}$ is presented. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> March 21, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="./Gutik_mine.html">O. Gutik</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> The semigroup of partial co-finite isometries of positive integers, II </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> The semigroup $\mathbf{I}\mathbb{N}_{\infty}$ of all partial co-finite isometries of positive integers is discussed. We proved that a congruence on the semigroup $\mathbf{I}\mathbb{N}_{\infty}$ is group if and only if its restriction onto an isomorphic copy of the bicyclic semigroup in $\mathbf{I}\mathbb{N}_{\infty}$ is a group congruence. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> March 28, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="./Gutik_mine.html">O. Gutik</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> On group congruences of inverse semigroups whose contain the semigroup of partial co-finite isometries of positive integers </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Let $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ be the the semigroup of cofinite monotone partial bijections of the set of pusitive integers $\mathbb{N}$ and $\mathbf{I}\mathbb{N}_{\infty}$ be the semigroup of all partial co-finite isometries of $\mathbb{N}$. We give a criterium when an inverse subsemigroup $S$ of $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathbf{I}\mathbb{N}_{\infty}$ has the following property: <b><i>every non-identity congruence of $S$ is a group congrunce</i></b>. We describe minimal inviverse subsemigroups with such property. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> April 4, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="https://www.bpp.agh.edu.pl/autor/plachta-leonid-06445">L. Plachta</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> On mesures of nonplanarity of cubic graphs </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We study two measures of nonplanarity of cubic graphs $G$, the genus $\gamma(G)$ and the edge deletion number $\mathbf{ed}(G)$. For cubic graphs of small order these parameters are compared with another measure of nonplanarity, the (rectiliniar) crossing number $\overline{\mathbf{cr}}(G)$. We introduce operations of connected sum, specified for cubic graphs $G$, and show that under certain conditions the parameters $\gamma(G)$ and $ed(G)$ are additive (subadditive) with respect to them. <br> The minimal genus graphs (i.e. the cubic graphs of minimum order with given value of genus $\gamma$) and the minimal edge deletion graphs (i.e. cubic graphs of minimum order with given value of edge deletion number $\mathbf{ed}$) are introduced and studied. We provide upper bounds for the order of minimal genus and minimal edge deletion graphs. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> April 11, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="./Gutik_mine.html">O. Gutik</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> On group congruences of inverse semigroups whose contain the semigroup of partial co-finite isometries of positive integers, II </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Let $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ be the the semigroup of cofinite monotone partial bijections of the set of pusitive integers $\mathbb{N}$ and $\mathbf{I}\mathbb{N}_{\infty}$ be the semigroup of all partial co-finite isometries of $\mathbb{N}$. We give a criterium when an inverse subsemigroup $S$ of $\mathcal{I}_{\infty}^{\!\nearrow}(\mathbb{N})$ such that $S$ contains $\mathbf{I}\mathbb{N}_{\infty}$ has the following property: <b><i>every non-identity congruence of $S$ is a group congrunce</i></b>. We describe minimal inviverse subsemigroups with such property. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> April 18, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Embedding of graph inverse semigroups into compact-like topological semigroups </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into d-compact topological semigroups. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> April 25, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Embedding of graph inverse semigroups into compact-like topological semigroups, II </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into d-compact topological semigroups. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> May 2, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Embedding of graph inverse semigroups into compact-like topological semigroups, III </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into d-compact topological semigroups. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> May 16, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> Embedding of graph inverse semigroups into compact-like topological semigroups, IV </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We investigate graph inverse semigroups which are subsemigroups of compact-like topological semigroups. More precisely, we characterise graph inverse semigroups which embeds densely into d-compact topological semigroups. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <tr> <td colspan=3 HEIGHT="12"> </td></tr> <tr> <td valign="top" width="25%"> <font size="+2"> July 19, 2018 </font><td valign="top" width="15%" > <b><font size="+2"> A. Ravsky </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> On the Koch problem </p> <UL type="square"><LI class='oItem'> <font size="+1"> <head> <script type="text/javascript" src="http://latex.codecogs.com/latexit.js"></script> <script type="text/javascript"> LatexIT.add('p',true); </script> </head> <p> We discuss on Koch's problem. In particular, we give a positive answer on Koch's problem in some partial cases. </p> </font></p> </div> </LI></UL></font></ul></tr> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> </table> <a href="https://plus.google.com/u/0/+OlegGutik"><img src="Rgplus-Gutik.jpg"></a> <a href="https://plus.google.com/u/0/+OlGutikPallady"><img src="Rgplus-Gutik.jpg"></a> <a href="https://plus.google.com/u/0/+TopologicalAlgebraSeminar"><img src="Rgplus-Gutik.jpg"></a> <br> <br> <!-- Start of StatCounter Code for Default Guide --> <script type="text/javascript"> var sc_project=9174828; var sc_invisible=0; var sc_security="d274098c"; var scJsHost = (("https:" == document.location.protocol) ? "https://secure." : "http://www."); document.write("<sc"+"ript type='text/javascript' src='" + scJsHost+ "statcounter.com/counter/counter.js'></"+"script>"); </script> <noscript><div class="statcounter"><a title="web analytics" href="http://statcounter.com/" target="_blank"><img class="statcounter" src="http://c.statcounter.com/9174828/0/d274098c/0/" alt="web analytics"></a></div></noscript> <!-- End of StatCounter Code for Default Guide --> <br> <!-- HotLog --> <script type="text/javascript"> hotlog_r=""+Math.random()+"&s=2303117&im=214&r="+ escape(document.referrer)+"&pg="+escape(window.location.href); hotlog_r+="&j="+(navigator.javaEnabled()?"Y":"N"); hotlog_r+="&wh="+screen.width+"x"+screen.height+"&px="+ (((navigator.appName.substring(0,3)=="Mic"))?screen.colorDepth:screen.pixelDepth); hotlog_r+="&js=1.3"; document.write('<a href="http://click.hotlog.ru/?2303117" target="_blank"><img '+ 'src="http://hit3.hotlog.ru/cgi-bin/hotlog/count?'+ hotlog_r+'" border="0" width="88" height="100" title="" alt="HotLog"><\/a>'); </script> <noscript> <a href="http://click.hotlog.ru/?2303117" target="_blank"><img src="http://hit3.hotlog.ru/cgi-bin/hotlog/count?s=2303117&im=214" border="0" width="88" height="100" title="" alt="HotLog"></a> </noscript> <!-- /HotLog --> </body> </html>