<!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_2010-2011</TITLE> <META content="text/html; charset=unicode" http-equiv=Content-Type> <META content="text/html; charset=iso-8859-1" http-equiv=??????????-???><!-- *************** DHTML Outline (begin) <META name="keywords" CONTENT="Oleg Gutik Igor Guran Olexander Ravsky Kateryna Pavlyk"> ***************** --> <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. 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Ravsky </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2>>=>C=0@=V 0;351@8: EB> 2>=8? <UL type=square> <LI class=oItem><FONT size=+1>C4CBL =02545=V @V7=><0=VB=V ?@8:;048 <>=>C=0@=8E 0;351@ 7 @V7=8E 30;C759 <0B5<0B8:8, 7>:@5<0 C @>1;5<V 3n+1, :>=25T2A:V9 3@V "8BBBO" B0 D@0:B0;0E. > >AB0==V< 42>< ?@8:;040< ?;0=CTBLAO  </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2> October 6, 2011, </br> October 13, 2011, </br> October 20, 2011 </FONT> <TD vAlign=top width="15%"><B><FONT size=+2>O. Ravsky </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2>The product of a nonempty family of pseudocompact paratopological groups is pseudocompact <UL type=square> <LI class=oItem><FONT size=+1>Will be proved the statement which is announced in the title. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2> Februaary 15, 2012 </FONT> <TD vAlign=top width="15%"><B><FONT size=+2>O. Ravsky </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> A specific example of a locally compact cancellative semigroup S which cannot be a subsemigroup of a paratopological group. <UL type=square> <LI class=oItem><FONT size=+1> Answering a next question of I. Guran we construct a locally compact Polish cancellative abelian semigroup S such that all shifts on S are quasi-open (that is, int (a+U) is non-empty for each element a\in S and each nonempty open subset U of S), but S cannot be a subsemigroup of a paratopological group. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2> Februaary 22, 2012 </FONT> <TD vAlign=top width="15%"><B><FONT size=+2>O. Ravsky </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> Each discrete subgroup of $S_\omega(X)$ is finite. <UL type=square> <LI class=oItem><FONT size=+1> Let $X$ be an infinite set and $S_\omega(X)$ be the group of all bijections of $X$ with finite supporter, endowed with the topology of the pointwise convergence. Inspired by the talk with I. Guran, we show that each discrete subgroup of $S_\omega(X)$ is finite. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2> Februaary 29, 2012, <br/> March 7, 2012, <br/> March 14, 2012, <br/> March 21, 2012, <br/> March 28, 2012, <br/> April 4, 2012 </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 monoids of injective partial cofinite selfmaps. <UL type=square> <LI class=oItem><FONT size=+1> We discuss on the semigroup $\mathscr{I}^{\mathrm{cf}}_\lambda$ of injective partial cofinite selfmaps of infinite cardinal $\lambda$. We show that $\mathscr{I}^{\mathrm{cf}}_\lambda$ is a bisimple inverse semigroup and for every non-empty chain $L$ in $E(\mathscr{I}^{\mathrm{cf}}_\lambda)$ there exists an inverse subsemigroup $S$ of $\mathscr{I}^{\mathrm{cf}}_\lambda$ such that $S$ is isomorphic to the bicyclic semigroup and $L\subseteq E(S)$, we describe the Green relations on $\mathscr{I}^{\mathrm{cf}}_\lambda$ and we prove that every non-trivial congruence on $\mathscr{I}^{\mathrm{cf}}_\lambda$ is a group congruence. We also prove that every Hausdorff locally compact topology $\tau$ on $\mathscr{I}^{\mathrm{cf}}_\lambda$ such that $(\mathscr{I}^{\mathrm{cf}}_\lambda,\tau)$ is a semitopological semigroup, is discrete and we describe the closure of the discrete semigroup $\mathscr{I}^{\mathrm{cf}}_\lambda$ in a topological semigroup. Finally, we show that the (discrete) semigroup $\mathscr{I}^{\mathrm{cf}}_\lambda$ cannot embed into a compact-like topological semigroup for any infinite cardinal $\lambda$, and we construct two non-discrete Hausdorff topologies which turn $\mathscr{I}^{\mathrm{cf}}_\lambda$ into a topological inverse semigroup. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2> Agust 6, 2012, <br/> Agust 8, 2012 </FONT> <TD vAlign=top width="15%"><B><FONT size=+2> Kateryna Pavlyk (University of Tartu, Estonia) <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> Pseudocompact topological Brandt $\lambda^0$-extensions of semitopological semigroups <UL type=square> <LI class=oItem><FONT size=+1> We introduce pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt $\lambda^0$-extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological semigroups in the class of semitopological semigroups and establish the structure of such extensions. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <TR> <TD height=12 colSpan=3></TD></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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