

October 10, 2012
 I.
Guran, O.
Gutik

 Divertisement
 The active participants of the seminar
were discuss new results and posed some open problems.




October 24, 2012
 O. Ravsky

 Divertisement
 The active participants of the seminar
were discuss new results and posed some open problems.




October 31, 2012, November 7, 2012, November 21, 2012,
November 28, 2012, December 5, 2012
 I.
Guran

 On nontopologized groups

The reporter discusses on the construction of a nontopologized group and related topics.




December 12, 2012
 I.Pozdnyakova

 On the monoid of cofinite monotone partial bijections of
nx_{lex}Z

The reporter discusses on the lattice of congruences of the monoid of cofinite monotone partial bijections of
nx_{lex}Z.




January 17, 2013, January 21, 2013
 O.
Gutik


Pseudocompact primitive topological inverse semigroups

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.



January 28, 2013
 O.
Gutik


On semitopological semigroup C

In the report we discuss on embeddings of the semigroup
C=< a,b  a^{2 }b=a, ab^{ 2 }=b> into
compactlike topological (semitopological) semigroups.



February 20, 2013
 I.
Guran, O.
Gutik

 Divertisement
 The active participants of the seminar
were discuss new results and posed some open problems.



March 27, 2013
 O. Ravsky


Different classes of bounded topological groups

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.



June 27, 2013
 O. Ravsky


On continuity of group operations

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.



July 2, 2013
 O. Ravsky


On continuity of group operations, II

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.
We shall continue the survey. In particular: We shall consider when a paratopological group is a
topological group; we recall related Sspaces 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_1compact semigroups the solution if the problem is independent of (ZFC+\frak c=\omega_2).



July 4, 2013
 O. Ravsky


On continuity of group operations, III

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.
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_1compact semigroups the solution if the
problem is independent of (ZFC+\frak c=\omega_2).



August 6, 2013
 O. Ravsky


Pseudocompactness is 3space property for paratopological groups

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.




August 9, 2013
 O.
Gutik


Group actions and the Brandt λ^{0}extensions of monoids with zero

We establish isomorphisms of the Brandt λ^{0}extensions of monoids with zeros and describe a category whose objects are ingredients in the constructions of the Brandt λ^{0}extensions of monoids with zeros and morphisms are isomorphisms of so extensions.




August 14, 2013
 O.
Gutik


On adjoining zero to a paratopological group and preserving pseudocompactness by products in some classes of (semi)topological semigroups

We discuss the topics presented in the title of the report.




August 15, 2013
 T. Banakh


Means on scattered compacta

We shall prove that a separable scattered compact space
containing a cocountable subset homeomorphic to [0, ω_{1}] admits
no separately continuous mean and no diagonally continuous nmean
for n ≥ 2.


