<!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_2013-2014</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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Ravsky </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> The example of a pseudocompact paratopological group which is not topological <UL type=square> <LI class=oItem><FONT size=+1> We present a functionally Hausdorff second countable paratopological group <i><b>G</b></i> such that each power of <i><b>G</b></i> is countably pracompact but <i><b>G</b></i> is not a topological group. We discuss some questions from descriptive topology related with the cardinal invariants of the constructed examples. </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>September 19, 2013 </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>,<BR><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>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></LI></UL></FONT></DIV></TD> </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>September 26, 2013 </FONT> <TD vAlign=top width="15%"><B><FONT size=+2>Sz. Gl&#261;b <br> F. Strobin </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> Large free subgroups of automorphisms groups of ultrahomogeneous spaces <UL type=square> <LI class=oItem><FONT size=+1> We consider the following largeness notion of subgroups of the symmetric group S<sub>&infin;</sub>. A group G is large if it contains a free subgroup with <b>c</b> generators. We give a necessary condition for a countable structure A to have the large automorphism group Aut(A). We also prove that under this condition any non-meager subgroup of Aut(A) with the Baire property is also large. It turns out that any countable free subgroup of S<sub>&infin;</sub> is contained in a large free subgroup of S<sub>&infin;</sub>, and under Martin's Axiom any free subgroup of S<sub>&infin;</sub> of cardinality less than continuum is contained in a large free subgroup of S<sub>&infin;</sub>. Finally, we show that the countable product of finitely generated groups either is large or else contains no uncountable free subgroup. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>September 27, 2013 </FONT> <TD vAlign=top width="15%"><B><FONT size=+2>A. Bartoszewicz </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> Multigeometric sequences, Cantors and Cantorvals <UL type=square> <LI class=oItem><FONT size=+1> For an absolute summing sequence x=(x<sub>n</sub>) by E(x) we denote the set of all sumsums of the series &Sigma;<sub>n</sub>x<sub>n</sub>. It is known that the set E(x) is one of the following forms: a finite union of closed intervals, a copy of the Cantor set, or so-called Cantorvals. We describe families of sequences which contain, according to our knowledge, all known examples of sequences x with Cantorval sumset E(x). Also, we give a sufficient condition for E(x) being Cantor. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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 3, 2013 </FONT> <TD vAlign=top width="15%"><B><FONT size=+2>I. Pozdnyakova </FONT></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> On generators and automorphizms of the the monoid of cofinite monotone partial bijections of L</FONT><sub><font size=-1>n</font></sub><FONT size=-1>x</A></FONT><sub><font size=-1>lex</font></sub><font size="+2">Z <UL type=square> <LI class=oItem><FONT size=+1> The reporter discusses on the generators and automorphisms of the the monoid of cofinite monotone partial bijections of L</FONT><sub><font size=-1>n</font></sub><FONT size=-1>x</A></FONT><sub><font size=-1>lex</sub></font><font size=+1>Z<font size=-1></font>. In particular this semigroup has four generators and all its automorphisms are inner. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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 10, 2013, <br> October 24, 2013</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> The structure of compact rings <UL type=square> <LI class=oItem><FONT size=+1> First we give some preliminary results, including a summary of Jacobson's Radical Theory in a form convenient for our use, some remarks on Q-rings (rings in which elements near zero are quasi-regular), and the abstract theory of boundedness. The structure theorems for compact rings are given. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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 31, 2013, <br> November 7, 2013, <br> November 14, 2013 </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> Korovin's example of a pseudocompact Tychonoff semitopological group which is not paratopological <UL type=square> <LI class=oItem><FONT size=+1> At last we shall know the construction of this example. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>November 21, 2013,<br> December 5, 2013 </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> An unexpected obstacle for the building of close to compact semi- and para-topological groups without automatic continuity of operations <UL type=square> <LI class=oItem><FONT size=+1> We show that if <b>(G,&#963)</b> is a Hausdorff precompact topological group, <b>(G,&#964)</b> is a paratopological or semitopological group with a base consisting of canonically open sets and <b>&#964&#8834&#963</b> then <b>(G,&#964)</b> is a topological group. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>February 6, 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> Pseudocompactness, products and Brandt &#955<sup><font size=-1>0</font></sup>-extensions <UL type=square> <LI class=oItem><FONT size=+1> We give conditions under which the Tychonoff product of topological Brandt &#955<sup><font size=-1>0</font></sup>-extensions of pseudocompact (countably compact) semitopological semigroups is a pseudocompact (countably compact) space. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>February 6, 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 H-complete topological inverse semigroups <UL type=square> <LI class=oItem><FONT size=+1> We consider a category of Lawson semilattices with compact maximal chains, and give sufficient conditions to be H-compete for such semilattices. Also it will be given sufficient conditions to be H-complete for some clases of topological inverse semigroups. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>February 13, 2014,<br> February 27, 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 H-complete topological inverse semigroups <UL type=square> <LI class=oItem><FONT size=+1> We consider topological inverse semigroups and give sufficient conditions to be H-complete in some classes of topological inverse semigroups. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>March 6, 2014,<br> March 13, 2014,<br> March 20, 2014</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> Sequentially pseudocompact spaces <UL type=square> <LI class=oItem><FONT size=+1> We reintroduce sequentially pseudocompact spaces which lie between sequentially compact and pseudocompact spaces and investigate their examples and properties with respect to standard operations with topological spaces. In particular, sequentially pseudocompact spaces unexpectedly turned out to be preserved by products, opposite to their above counterparts. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>March 27, 2014,<br> April 3, 2014</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> Extrasensory perception strategy and Catalan numbers <UL type=square> <LI class=oItem><FONT size=+1> The speaker, after the years of his practice of ancient mystic teachings, is going to reveal mathematical mysteries. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>April 24, 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 topological semilattices with compact maximal chains <UL type=square> <LI class=oItem><FONT size=+1> The speaker descusses on the structure and properties of topological semilattices with compact maximal chains. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>May 15, 2014</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> Cone topologies of paratopological groups <UL type=square> <LI class=oItem><FONT size=+1> We begin a cycle of lectures devoted to the subject which is useful for constructing counterexamples of paratopological groups. We start from an interplay between the algebraic properties of the cone semigroup S and compact-like properties of two semigroup topologies generated by S on the group. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>May 22, 2014, <br> June 19, 2014, <br> June 27, 2014, <br> July 3, 2014, <br> July 21, 2014 </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> Cone topologies of paratopological groups <UL type=square> <LI class=oItem><FONT size=+1> We continue the cycle of lectures devoted to the subject which is useful for constructing counterexamples of paratopological groups. We start from an interplay between the algebraic properties of the cone semigroup S and compact-like properties of two semigroup topologies generated by S on the group. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>August 4, 2014, <br>August 6, 2014, <br>August 8, 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> Topological algebraic and categorical properties of the polycyclic monoid <UL type=square> <LI class=oItem><FONT size=+1> We describe a subsemillatice of the polycyclic monoid, constract a minimal topology on the polyciclic monoid and prove that polycyclic monoid in this topology is an H-complete topological inverse semigroup. Also we study some topological, algebraic and categorical properties of the polycyclic monoid. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>August 22, 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 compactly factorizable topological inverse semigroups <UL type=square> <LI class=oItem><FONT size=+1> We discuss on compactly factorizable topological inverse semigroups and related topics. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <TR> <TD height=12 colSpan=3></TD></TR> <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>August 27, 2014</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> On completeness of topological inverse semigroups <UL type=square> <LI class=oItem><FONT size=+1> We discuss on completeness of topological inverse semigroups which is a generalization of the Raikov completeness for topological groups. </LI></UL></FONT></LI></UL></FONT></DIV></TD> <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> <!-- 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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