<html> <head> <title>Lviv seminar on Topological Algebra archivta_2009-2010</title> <Base > <meta http-equiv="??????????-???" content="text/html; charset=iso-8859-1"> <META name="keywords" CONTENT="Oleg Gutik Igor Guran Olexander Ravsky"> <!-- *************** DHTML Outline (begin) ***************** --> <STYLE TYPE='text/css'> <!-- /*Define elements with children with the class='outlineParentItem', and all elements without children with class='outlineItem'*/ 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://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/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_ta08_09.html"><img src="left.gif"></a> </b><i>Archive for</i><b> <font size="+2">(2009/2010)</font> </b><i>academic year</i></b></font> <a href="seminararchiv_ta10_11.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"> October 8, 2009 </font><td valign="top" width="15%" > <b><font size="+2"> <a href="guran.html">I. Guran</a>,<br> <a href="Gutik_mine.html">O. Gutik</a>,<br> O. Ravsky </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 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"> October 15, 2009,<br> October 22, 2009,<br> October 29, 2009 </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"> Topological semigroups of cofinite monotone bijective partial transformations of positive integers <UL type="square"><LI class='oItem'> <font size="+1"> We show that the semigroup of partial cofinal monotone bijective transformations of the set of positive integers has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology on the semigroup of partial cofinal monotone bijective transformations of the set of positive integers S such that S is a topological inverse semigroup is discrete and we describe the closure of S in a topological semigroup. </LI></UL></font></ul></tr> <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"> November 12, 2009 </font><td valign="top" width="15%" > <b><font size="+2"> A. Reiter </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On H-closed Clifford topological inverse semigroups <UL type="square"><LI class='oItem'> <font size="+1"> We show that an arbitrary Clifford topological inverse semigroup with an algebraic closed maximal subsemilattice and H-closed maximal subgroups is H-closed in the class of topological inverse semigroups. </LI></UL></font></ul></tr> <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"> November 19, 2009 </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"> On H-closed inverse semigroup topologies on the semigroup of finite partial bijections of a bounded finite rank <UL type="square"><LI class='oItem'> <font size="+1"> We show that the topological inverse semigroup of finite partial bijections of a bounded finite rank <b><i>I</i><sub>&lambda;</sub><sup>n</sup></b> is H-closed if and only if its band <b><i>E(I</i><sub>&lambda;</sub><sup>n</sup>)</b> is compact. Also we construct H-closed semigroup topology on <b><i>I</i><sub>&lambda;</sub><sup>n</sup></b> such that the band <b><i>E(I</i><sub>&lambda;</sub><sup>n</sup>)</b> is a discrete subspace of <b><i>I</i><sub>&lambda;</sub><sup>n</sup></b>. </LI></UL></font></ul></tr> <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"> November 26, 2009,<br> December 24, 2009 </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"> On chains in H-closed topological pospaces <UL type="square"><LI class='oItem'> <font size="+1"> We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space (H-closed topological semilattice) under which L contains a maximal (minimal) element. We also give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that a linearly ordered H-closed topological semilattice is an H-closed topological pospace and show that in general, this is not true. We construct an example of an H-closed topological pospace with a non-H-closed maximal chain and give sufficient conditions under which a maximal chain of an H-closed topological pospace is an H-closed topological pospace. </LI></UL></font></ul></tr> <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"> February 18, 2010 </font><td valign="top" width="15%" > <b><font size="+2"> <a href="guran.html">I. Guran</a>,<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"> 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> <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"> February 25, 2010,<br> March 4, 2010,<br> March 11, 2010 </font><td valign="top" width="15%" > <b><font size="+2"> <a href="guran.html">I. Guran</a>,<br> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On a metrizability of cancellative topological semigroups <UL type="square"><LI class='oItem'> <font size="+1"> We discuss on a metrizability of cancellative topological semigroups. </LI></UL></font></ul></tr> <tr> <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"> March 18, 2010 </font><td valign="top" width="15%" > <b><font size="+2"> <a href="guran.html">I. Guran</a>,<br> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Koch Problem on monothetic topological semigroups <UL type="square"><LI class='oItem'> <font size="+1"> We give the sufficient conditions on a locally compact topological semigroup under which the Pontryagin Alternative holds. </LI></UL></font></ul></tr> <tr> <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"> March 25, 2010 </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"> On a finite symmetric inverse semigroup of bounded rank <UL type="square"><LI class='oItem'> <font size="+1"> We describe all congruences on a finite symmetric inverse semigroup of bounded rank and show that it is algebraically h-closed in the class in semitopological inverse semigroups with continuous inversion. </LI></UL></font></ul></tr> <tr> <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"> April 1, 2010 </font><td valign="top" width="15%" > <b><font size="+2"> <a href="http://www.logic.univie.ac.at/~lzdomsky/">L. Zdomskyy</a> </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> <a href="http://www.math.uni-bonn.de/people/logic/events/young-set-theory-2010/Zdomskyy.pdf">On maximal almost disjoint families</a> <UL type="square"><LI class='oItem'> <font size="+1"> The talk will be devoted to different types of maximal almost disjoint families. In particular, several constructions of strongly maximal almost disjoint families of functions will be presented. </LI></UL></font></ul></tr> </LI></UL></font></ul></tr> <tr> <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"> April 8, 2010 </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"> On compact topologies on a finite symmetric inverse semigrou of bounded rank <UL type="square"><LI class='oItem'> <font size="+1"> We describe all compact and countable compact Hausdorff topologies on a finite symmetric inverse semigroup of bounded rank <b><i>I</i><sub>&lambda;</sub><sup>n</sup></b> such that <b><i>I</i><sub>&lambda;</sub><sup>n</sup></b> is a semitopological semigroup. </LI></UL></font></ul></tr> <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"> April 29, 2010 </font><td valign="top" width="15%" > <b><font size="+2"> I. Pastukhova </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> Continuously cancellative Clifford inverse topological semigroups. <UL type="square"><LI class='oItem'> <font size="+1"> We prove that a Clifform inverse topological semigroup S whose idempotent band E is a U-semilattice embeds into a compact Clifford topological inverse semigroup with zero-dimensional band if and only if <ol> <li> E embeds into a zero-dimensional compact semilattice; <li> the maximal subgroups H<sub>e</sub> of S are totally bounded; <li> S is continuously cancellative. </ol> A Clifford topological inverse semigroup S is called <i>continuously cancellative</i> is for each point x in S and a neighborhood O(x) there are neighborhoods U(x) and O(e) of the idempotent e=xx<sup>-1</sup> such that a point y of S belongs to the neighborhood O(x) provided yy<sup>-1</sup> lies in O(e) and ye lies in U(x). <td> <font size="+1"> </LI></UL></font></ul></tr> <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"> May 6, 2010 </font><td valign="top" width="15%" > <b><font size="+2"> I. Chuchman </font></b> <td valign="center"><DIV onClick="JavaScript: outlineAction();"> <ul type="square"><LI class='oParent' value="30"> <font size="+2"> On a semigroup of almost monotone partial bijective transformations of positive intergers. <UL type="square"><LI class='oItem'> <font size="+1"> We discuss on algebraic properties of the semigroup of almost monotone partial bijective transformations of positive intergers ant its topologizations as semitopological and topological semigroups. <td> <font size="+1"> </LI></UL></font></ul></tr> <tr><td colspan=3 HEIGHT="3" BORDER="1" ALIGN="left" bgcolor="#000080" ></tr> </table> <br> <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> <!-- 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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