<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <!-- saved from url=(0089)http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/seminararchiv_ta10_11.html --> <HTML><HEAD><TITLE>Lviv seminar on Topological Algebra archivta_2014-2015</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. 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Gutik</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Divertisement <UL type="square"><LI class='oItem'> <font size="+1"> The active participants of the seminar were discuss new results and posed some open problems. </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 10, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Divertisement <UL type="square"><LI class='oItem'> <font size="+1"> The active participants of the seminar were discuss new results and posed some open problems. </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 17, 2014, <br> October 1, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/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"> On closures in semitopological inverse semigroups with continuous inversion <UL type="square"><LI class='oItem'> <font size="+1"> We discuss on the closures of subgroups, semilattices and different kinds of semigroup extensions in semitopological inverse semigroups with continuous inversion. In particularly we show that a topological group <b>G</b> is <b>H</b>-closed in the class of semitopological inverse semigroups with continuous inversion if and only if <b>G</b> is compact, a Hausdorff linearly ordered topological semilattice <b>E</b> is <b>H</b>-closed in the class of semitopological semilattices if and only if <b>E</b> is <b>H</b>-closed in the class of topological semilattices, and a topological Brandt <b>&#955<sup><font size=-1>0</font></sup></b>-extension of <b>S</b> is (absolutely) <b>H</b>-closed in the class of semitopological inverse semigroups with continuous inversion if and only if so is <b>S</b>. Also, we construct an example of an <b>H</b>-closed semitopological semilattice in the class of semitopological semilattices which is not absolutely <b>H</b>-closed in the class of semitopological semilattices. </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 8, 2014, <br> October 15, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On <b>H</b>-closed quasitopological groups <UL type="square"><LI class='oItem'> <font size="+1"> We should prove that each Cauchy compete Hausdorff quasitopological group is <b>H</b>-closed in the class of Hausdorff quasitopological groups. In particular, a Hausdorff topological group <b>G</b> is <b>H</b>-closed in the class of Hausdorff quasitopological groups iff <b>G</b> is Raikov complete. </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 22, 2014, <br> October 29, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Cowide topologies and their applications <UL type="square"><LI class='oItem'> <font size="+1"> TBA </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 12, 2014, <br>November 19, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/Gutik_mine.html">O. Gutik</A>, <br> K. Mel'nyk </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On the semigroup of co-finite momotone partial bijections of the real line <UL type="square"><LI class='oItem'> <font size="+1"> We discusss on the structure of the semigroup of co-finite momotone partial bijections of the real line. </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 26, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/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"> On <b>H</b>-closed pospaces without infinite antichains <UL type="square"><LI class='oItem'> <font size="+1"> We describe the topology of an <b>H</b>-closed pospace without infinite antichains and show that an <b>H</b>-closed pospace without infinite antichains is monotone normal. </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 3, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> An introduction to <b>H</b>-closed quasitopological groups <UL type="square"><LI class='oItem'> <font size="+1"> See the title. :-) Also we show that a topological group <b>G</b> is <b>H</b>-closed in the class of quasitopological groups if and only if <b>G</b> is Raikov complete and present some examples. </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 29, 2014 </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"> On the k-polycyclic monoid <UL type="square"><LI class='oItem'> <font size="+1"> For every cardinal k we intriduce a notion of the k-polycyclic monoid and study it's topological properties as a topological inverse semigroup. For evere positive integer n we constract a minimal topology on the n-polycyclic monoid and prove that with this topology it is a H-complete topological inverse semigroup. </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 30, 2014 </font><td valign="top" width="15%" > <b><font size="+2"> O. Chervak </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On some asymptotic bounds for Ramsey numbers <UL type="square"><LI class='oItem'> <font size="+1"> We will discuss some new bounds for diagonal and off-diagonal Ramsey numbers. </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 13, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/bancv.html">T. Banakh</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> A natural uniformity on a paratopological group <UL type="square"><LI class='oItem'> <font size="+1"> We prove that each (Hausdorff) paratopological group <b>G</b> carries a natural (separated) uniformity turning <b>G</b> into a uniform quasi-topological group. This uniformity is generated by the base consisting of the sets <b>{(x,y)&#8712; G&#215;G: y&#8712; VxV<sup>-1</sup>&#8745;V<sup>-1</sup>xV}</b> where V runs over neighborhoods of the unit in <b>G</b>. The presence of this uniqformity guarantees that each Hausdorff paratopologial group <b>G</b> condences onto a Tychonoff quasi-topological group and so <b>G</b> is functionally Hausdorff. If <b>G</b> is countably Hausdorff, then <b>G</b> condences onto a metrizable quasi-topological group and hence is submetrizable. This resolves two probelsm of Arkhangelski and Tkachenko. More details can be found <a href="http://arxiv.org/abs/1409.4167">here</a>. </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 16, 2015 </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"> On an embedding of the polycyclic monoid <UL type="square"><LI class='oItem'> <font size="+1"> We prove that for every non zero cardinal k the k-Polycyclic monoid does not embed into any countably compact topologycal semigroup. </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 11, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Divertisement <UL type="square"><LI class='oItem'> <font size="+1"> We started a new spring session of our seminar from the Divertisment. The active participants of the seminar are discussed new results and they posed some open problems. </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 18, 2015 </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"> Some remarks on topologizations of the polycyclic monoid <UL type="square"><LI class='oItem'> <font size="+1"> We built locally compact non discrete topology <b>&#428;</b> on the <b>k</b>-polycyclic monoid <b>P</b> such that <b>(P,&#428;)</b> is topologycal inverse semigroup. Also we proved, that <b>Y&#92;P</b> is a ideal for every semitopological semigroup <b>Y</b> such that <b>cl(P)=Y</b>, and construct a compact topology <b>&#430;</b> on P such that <b>(P,&#430;)</b> is a semitopologycal semigroup. </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 25, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/guran.html">I. Guran</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On boundedness of topological rings <UL type="square"><LI class='oItem'> <font size="+1"> We consider various types of boundedness in topological rings: precompact, &#964;-narrow, ets. Cardinal functions are investigated. </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 4, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/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"> On some problems on topological graph semigroups and infinite word semigroups <UL type="square"><LI class='oItem'> <font size="+1"> Some problems on topological graph semigroups and infinite word semigroups were posed. </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 11, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/guran.html">I. Guran</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On boundedness of topological rings <UL type="square"><LI class='oItem'> <font size="+1"> We consider various types of boundedness in topological rings: precompact, &#964;-narrow, ets. Cardinal functions are investigated. </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 25, 2015 </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"> On a completion of quasitopological grups <UL type="square"><LI class='oItem'> <font size="+1"> We consider a completion <b>G*</b> of a quasitopologycal group <b>G</b> and prove that <b>G*</b> is an <b>H</b>-closed quasitopologycal group. Moreover <b>G</b> is a dense subgroup of <b>G*</b>. </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 1, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Characteristic subsets of locally compact abelian topological groups <UL type="square"><LI class='oItem'> <font size="+1"> A subset $A$ of a locally compact abelian topological group $G$ we shall call *characteristic*, if there is no sequence $\{\phi_k\}$ of non-trivial characters of the group $G$ such that $\{\phi_k(a)\}$ converges to the unit for each element $x\in A$. Investigating the problem which subsets $A$ are characteristic, we obtain some beginning results and pose some problems and directions of investigation. </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 7, 2015 </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"> On a completion of quasitopological grups <UL type="square"><LI class='oItem'> <font size="+1"> We consider a completion <b>G*</b> of a quasitopologycal group <b>G</b> and prove that <b>G*</b> is an <b>H</b>-closed quasitopologycal group. Moreover <b>G</b> is a dense subgroup of <b>G*</b>. </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 15, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/guran.html">I. Guran</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On boundedness of topological rings <UL type="square"><LI class='oItem'> <font size="+1"> We consider various types of boundedness in topological rings: precompact, &#964;-narrow, ets. Cardinal functions are investigated. </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 22, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> S. Bardyla, </br> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> @> =01>;V;5 B0 28<CG5=5. Bardyla Theorem. <UL type="square"><LI class='oItem'> <font size="+1"> <b>?V3@0D: <i>"845; 5=8= ?0H=8, 871K 45@525=L, 2845; >= 2G5@0H=89 8 3@O4CI89 45=L!"</i></b></br> (&5 - =5 @5:;0<0 :><C=V7<C, F5 - =>AB0;L3VO 70 =54>2545=>N !5@L>65=L:>N B5>@5<>N!) </br> Inspired and filling the small gap by the first speaker, he and the second speaker proved that if <b>(G,&#964;)</b> is a Cauchy full quasitopological group, <b>(G,&#963;)</b> is a quasitopological group, <b>&#963;&#891;&#964;</b>, and the space <b>(G,&#963;)</b> has a <b>&#960;</b>-base, consisting of open in the space <b>(G,&#964;)</b> subets then <b>(G,&#963;)</b> is a Cauchy full quasitopological group too. </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 6, 2015, </br> May 13, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/bancv.html">T. Banakh</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <b>k</b>-Spaces, their generalizations and applications <UL type="square"><LI class='oItem'> <font size="+1"> We consider some generalizations of the <b>k</b>-space property and discuss their applications to free constructions of topological algebra. </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"> June 3, 2015, </br> June 10, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/Karchevska.html">L. Karchevska</A>, </br> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/bancv.html">T. Banakh</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On metrization of functors <UL type="square"><LI class='oItem'> <font size="+1"> We discuss the problem of metrization of functional functors and functors with finite supports. </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"> June 17, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/bancv.html">T. Banakh</A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Cardinal invariants distinguishing permutation groups <UL type="square"><LI class='oItem'> <font size="+1"> We prove that for infinite cardinals <b>&#x3BA;<&#x3BB;</b> the alternating group <b>Alt(&#x3BB;)</b> (of even permutations) of <b>&#x3BB;</b> is not embeddable into the symmetric group <b>Sym(&#x3BA;)</b> (of all permutations) of <b>&#x3BA;</b>. To prove this fact we introduce and study several monotone cardinal group invariants which take value <b>&#x3BA;</b> on groups <b>Alt(&#x3BA;)</b> and <b>Sym(&#x3BA;)</b>. </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"> June 18, 2015 </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"> On a completeness of factorizable topological inverse semigroups <UL type="square"><LI class='oItem'> <font size="+1"> We study a completeness of factorizable topological inverse semigroups and introduce a method how to construct such semigroups. </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"> June 30, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> . 0B>: </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> 5:>B>@K5 A2O78 <564C B>?>;>3859 8 48=0<8:>9 <UL type="square"><LI class='oItem'> <font size="+1"> K @0AA<>B@8< =5:>B>@K5 A2O78 <564C B>?>;>3859 48DD5@5=F8@C5<>3> <=>3>>1@078O 8 A2>9AB20<8 8=48284C0;L=KE 48DD5><>@D87<>2 8 3@C?? 48DD5><>@D87<>2 MB>3> <=>3>>1@078O. ;0AA8G5A:85 @57C;LB0BK B0:>3> @>40 >B=>AOBAO : A2>9AB20< ?5@8>48G5A:8E >@18B. @8<5@K: D>@<C;0 A;540 5DH5F0, B5>@8O 8;LA5=0. ! @0728B85< 38?5@1>;8G5A:>9 48=0<8:8 2 ?>A;54=85 ?>;25:0 ?>O28;8AL @57C;LB0BK, :>B>@K5 30@0=B8@CNB ACI5AB2>20=85 A;>6=KE 8=20@80=B=KE <=>65AB2 A 25AL<0 =5B@8280;L=>9 48=0<8:>9.  ?>A;54=85 10 ;5B >1=0@C68;8AL 25AL<0 C4828B5;L=K5 A2>9AB20 :><<CB0B82=KE 3@C?? 48DD5><>@D87<>2 @0=30 1>;LH5 548=8FK. </br> 5>1E>48<K5 ?>=OB8O 87 B5>@88 48=0<8G5A:8E A8AB5< 1C4CB >1JOA=5=K. </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 6, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/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"> On the dichotomy of a locally compact semitopological bicyclic monoid with adjoined zero <UL type="square"><LI class='oItem'> <font size="+1"> We show that that if <b>&tau;</b> be a Hausdorff locally compact topology on the bicyclic semigroup with adjoined zero <b><i>C</i><sup><font size=-1> 0</font></sup> = <i>C</i>(p,q)&#8746;{0}</b> such that <b>(<i>C</i><sup><font size=-1> 0</font></sup>,&tau;)</b> is a semitopological semigroup, then <b>&tau;</b> is either compact or discrete. </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 14, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> O. 02AL:89 </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> >2V ?@83>48 :>=O B0 2VA;NG:0 <UL type="square"><LI class='oItem'> <font size="+1"> VA;NG>: @>7:065 ?@> A2>N 206:C 4>;N 157 :>=O. V= =048102 O1;CG:> B0 CA5 2V4 =L>3> 2V4:CHCT, 2V4:CHCT, 0;5 =VO: =5 ?@>:>2B=5. VA;NG>: BO3=5BLAO 4> O1;CG:0 B0 ?V4AB@81CT, 0;5 B@510 :>=O, 1> C <5=5 =5 :V=AL:V A8;8, 0 ;8H5 2VA;NGV. <br> <img src="oslik.jpg"> </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 20, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/Gutik_mine.html">O. Gutik</A>, <br> K. Melnyk </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On the structure of the semigroup of co-finite momotone partial homeomorphisms of the real line <UL type="square"><LI class='oItem'> <font size="+1"> We describe the structure of the semigroup of co-finite momotone partial homeomorphisms of the real line. </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 28, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> <A href="http://imath.kiev.ua/~lub/">. N10H5=:></A> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <b>K</b>-B5>@VO: <b>Q</b>-:>=AB@C:FVO 28;5=0 <UL type="square"><LI class='oItem'> <font size="+1"> 5@5?>2V40TBLAO <b>Q</b>-:>=AB@C:FVO 28;5=0 4;O B>G=8E :0B53>@V9 <b>A</b>. > B0:V9 1C4CTBLAO :0B53>@VO <b>QA</b> V WW :;0A8DV:CNG89 ?@>ABV@ <b>BQA</b>. 8IV <b>K</b>-3@C?8 287=0G0NBLAO O: 3><>B>?VG=V 3@C?8 <b>BQA</b>. </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 30, 2015, </br> July 31, 2015, </br> August 3, 2015 </font><td valign="top" width="15%" > <b><font size="+2"> O. Ravskyi </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On extent of weakly submeta-Lindel&#246;f spaces <UL type="square"><LI class='oItem'> <font size="+1"> We discuss on the topic of the title. </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) ? 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