


September 12, 2013
 O. Ravsky


The example of a pseudocompact paratopological group which is not topological

We present a functionally Hausdorff second countable paratopological group G such that each power of G is countably pracompact but G is not a topological group. We discuss some questions from descriptive topology related with the cardinal invariants of the constructed examples.



September 19, 2013
 I.
Guran, O.
Gutik

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




September 26, 2013
 Sz. Gląb F. Strobin


Large free subgroups of automorphisms groups of ultrahomogeneous spaces

We consider the following largeness notion of subgroups of the symmetric group
S_{∞}. A group G is large if it contains a free subgroup with
c 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 nonmeager
subgroup of Aut(A) with the Baire property is also large. It
turns out that any countable free subgroup of S_{∞} is contained in a
large free subgroup of S_{∞}, and under Martin's
Axiom any free subgroup of S_{∞} of cardinality less than
continuum is contained in a large free subgroup of
S_{∞}.
Finally, we show that the countable product of
finitely generated groups either is large or else contains no uncountable
free subgroup.




September 27, 2013
 A. Bartoszewicz


Multigeometric sequences, Cantors and Cantorvals

For an absolute summing sequence x=(x_{n}) by E(x) we denote the set of all sumsums of the series Σ_{n}x_{n}. 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 socalled 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.




October 3, 2013
 I. Pozdnyakova


On generators and automorphizms of the the monoid of cofinite monotone partial bijections of L_{n}x_{lex}Z

The reporter discusses on the generators and automorphisms of the the monoid of cofinite monotone partial bijections of L_{n}x_{lex}Z. In particular this semigroup has four generators and all its automorphisms are inner.




October 10, 2013, October 24, 2013
 I. Guran


The structure of compact rings

First we give some preliminary results, including a summary of Jacobson's Radical Theory in a form convenient for our use, some remarks on Qrings (rings in which elements near zero are quasiregular), and the abstract theory of boundedness. The structure theorems for compact rings are given.




October 31, 2013, November 7, 2013, November 14, 2013
 O. Ravsky


Korovin's example of a pseudocompact Tychonoff semitopological group which is not paratopological

At last we shall know the construction of this example.




November 21, 2013, December 5, 2013
 O. Ravsky


An unexpected obstacle for the building of close to compact semi and paratopological groups without automatic continuity of operations

We show that if (G,σ) is a Hausdorff precompact topological group, (G,τ) is a paratopological or semitopological group
with a base consisting of canonically open sets and τ⊂σ then (G,τ) is a topological group.




February 6, 2014
 O. Gutik


Pseudocompactness, products and Brandt λ^{0}extensions

We give conditions under which the Tychonoff product of topological Brandt λ^{0}extensions of pseudocompact (countably compact) semitopological semigroups is a pseudocompact (countably compact) space.




February 6, 2014
 S. Bardyla


On Hcomplete topological inverse semigroups

We consider a category of Lawson semilattices with compact maximal chains,
and give sufficient conditions to be Hcompete for such semilattices.
Also it will be given sufficient conditions to be Hcomplete for some clases of topological inverse semigroups.




February 13, 2014, February 27, 2014
 S. Bardyla


On Hcomplete topological inverse semigroups

We consider topological inverse semigroups and give sufficient conditions to be Hcomplete in some classes of topological inverse semigroups.




March 6, 2014, March 13, 2014, March 20, 2014
 O. Ravsky


Sequentially pseudocompact spaces

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.




March 27, 2014, April 3, 2014
 O. Ravsky


Extrasensory perception strategy and Catalan numbers

The speaker, after the years of his practice of ancient mystic teachings, is going to reveal mathematical mysteries.




April 24, 2014
 S. Bardyla


On topological semilattices with compact maximal chains

The speaker descusses on the structure and properties of topological semilattices with compact maximal chains.




May 15, 2014
 O. Ravsky


Cone topologies of paratopological groups

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 compactlike properties of two semigroup topologies generated by S on the group.




May 22, 2014, June 19, 2014, June 27, 2014, July 3, 2014, July 21, 2014
 O. Ravsky


Cone topologies of paratopological groups

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 compactlike properties of two semigroup topologies generated by S on the group.




August 4, 2014, August 6, 2014, August 8, 2014
 S. Bardyla


Topological algebraic and categorical properties of the polycyclic monoid

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 Hcomplete topological inverse semigroup. Also we study some topological,
algebraic and categorical properties of the polycyclic monoid.




August 22, 2014
 S. Bardyla


On compactly factorizable topological inverse semigroups

We discuss on compactly factorizable topological inverse semigroups and related topics.




August 27, 2014
 T. Banakh


On completeness of topological inverse semigroups

We discuss on completeness of topological inverse semigroups which is a generalization of the Raikov completeness for topological groups.

