<!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_2012-2013</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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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> <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 24, 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>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> <TR> <TD bgColor=#000080 height=3 colSpan=3 align=left BORDER="1"></TD> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2>October 31, 2012,<br> November 7, 2012,<br> November 21, 2012, <br> November 28, 2012,<br> December 5, 2012</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></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2>On nontopologized groups <UL type=square> <LI class=oItem><FONT size=+1> The reporter discusses on the construction of a non-topologized group and related topics. </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 height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2>December 12, 2012</FONT> <TD vAlign=top width="15%"><B><FONT size=+2>I.Pozdnyakova</A></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2>On the monoid of cofinite monotone partial bijections of n<FONT size=-1>x</A></FONT><sub><font size=-1>lex</font></sub>Z <UL type=square> <LI class=oItem><FONT size=+1> The reporter discusses on the lattice of congruences of the monoid of cofinite monotone partial bijections of n<FONT size=-1>x</A></FONT><sub><font size=-1>lex</font></sub>Z. </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 height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2>January 17, 2013,<br> January 21, 2013</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></A></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> Pseudocompact primitive topological inverse semigroups <UL type=square> <LI class=oItem><FONT size=+1> In the report we discuss on pseudocompact primitive topological inverse semigroups. We describe the structure of pseudocompact primitive topological inverse semigroups and show that a Tychonoff product of a family of pseudocompact primitive topological inverse semigroups is a pseudocompact topological space. Also we prove that the Stone-\v{C}ech compactification of a pseudocompact primitive topological inverse semigroup is a compact primitive 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>January 28, 2013</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></A></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> On semitopological semigroup C <UL type=square> <LI class=oItem><FONT size=+1> In the report we discuss on embeddings of the semigroup C=< a,b | a<sup><font size=-1>2</font> </sup>b=a, ab<sup> <font size=-1>2</font> </sup>=b> into compact-like topological (semitopological) semigroups. </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>February 20, 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> <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, 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> Different classes of bounded topological groups <UL type=square> <LI class=oItem><FONT size=+1> Following the problems of I. Yo. Guran from the previous seminar, we impose different bound conditions on topological groups. We are trying to distinguish these conditions in different classes of topological groups and formulate new problems. </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>June 27, 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> On continuity of group operations <UL type=square> <LI class=oItem><FONT size=+1> Based on speaker's PhD thesis we start a cycle of lectures devoted to continuity of group operations in paratopological and semitopological groups, with an accent on game based proofs having in mind to apply them for proving that some inverse topological semigroups are topological inverse semigroups. </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>July 2, 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> On continuity of group operations, II <UL type=square> <LI class=oItem><FONT size=+1> Based on speaker's PhD thesis we start a cycle of lectures devoted to continuity of group operations in paratopological and semitopological groups, with an accent on game based proofs having in mind to apply them for proving that some inverse topological semigroups are topological inverse semigroups. <br> We shall continue the survey. In particular: We shall consider when a paratopological group is a topological group; we recall related S-spaces introduced by E. Reznichenko. We shall consider when a semitopological group G is a paratopological group; we shall deal with topological games and recall the positive Reznichenko's when (G,G) is a Grothendieck pair. We shall consider when a cancellative topological semigroup is a group: we shall recall Artur Hideyuki Tomita's result that for initially \omega_1-compact semigroups the solution if the problem is independent of (ZFC+\frak c=\omega_2). </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>July 4, 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> On continuity of group operations, III <UL type=square> <LI class=oItem><FONT size=+1> Based on speaker's PhD thesis we start a cycle of lectures devoted to continuity of group operations in paratopological and semitopological groups, with an accent on game based proofs having in mind to apply them for proving that some inverse topological semigroups are topological inverse semigroups. <br> We shall continue the survey. In particular: We shall consider when a semitopological group G is a paratopological group; we shall deal with topological games and recall the positive Reznichenko's when (G,G) is a Grothendieck pair. We shall consider when a cancellative topological semigroup is a group: we shall recall Artur Hideyuki Tomita's result that for initially \omega_1-compact semigroups the solution if the problem is independent of (ZFC+\frak c=\omega_2). </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>August 6, 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> Pseudocompactness is 3-space property for paratopological groups <UL type=square> <LI class=oItem><FONT size=+1> The speaker wishes to devote a couple of talks to his proof that a paratopological group G is pseudocompact provided G has a normal subgroup N such that both N and the quotient paratopological group G/N are pseudocompact. Remark: The result was obtained by the speaker during the last week and it positively solves more than 3/2 problems from the survey by Michail Tkachenko. So the listeners of the seminar will have the unique occasion to be the first persons in the world who will hear the solution. Acknowledgement: The speaker wishes to thank to Oleg Gutik who invited him for the talks. </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 height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2>August 9, 2013</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></A></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> Group actions and the Brandt &#955<sup><font size=-1>0</font></sup>-extensions of monoids with zero <UL type=square> <LI class=oItem><FONT size=+1> We establish isomorphisms of the Brandt &#955<sup><font size=-1>0</font></sup>-extensions of monoids with zeros and describe a category whose objects are ingredients in the constructions of the Brandt &#955<sup><font size=-1>0</font></sup>-extensions of monoids with zeros and morphisms are isomorphisms of so 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> <TR> <TD height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2>August 14, 2013</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></A></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> On adjoining zero to a paratopological group and preserving pseudocompactness by products in some classes of (semi)topological semigroups <UL type=square> <LI class=oItem><FONT size=+1> We discuss the topics presented in the title of the report. </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 height=12 colSpan=3></TD></TR> <TR> <TD vAlign=top width="25%"><FONT size=+2>August 15, 2013</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></A></B> <TD vAlign=center> <DIV onclick="JavaScript: outlineAction();"> <UL type=square> <LI class=oParent value=30><FONT size=+2> Means on scattered compacta <UL type=square> <LI class=oItem><FONT size=+1> We shall prove that a separable scattered compact space containing a cocountable subset homeomorphic to [0, &#969<sub>1</sub>] admits no separately continuous mean and no diagonally continuous n-mean for n &#8805 2. </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> <br> <P align=left> <IMG src="ta-12-13-part.jpg" width="939" height="704"border=2 name="img1" alt="The participants of the seminar. 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