
Date:

Speaker:

Title (click on the title to see the Abstract):



19.06.17

T.Banakh

Generalizing ProdanovStoyanov Theorem on minimal topological groups
We shall prove that an Abelian topological group is compact if and only if it is complete in each weaker group topology.







12.06.17

T.Banakh

Detecting Hclosed topological groups
We shall discuss the recent progress in the problem of detecting topological groups which are (absolutely or injectively) Hclosed in some classes of topological semigroups.
More details can be found in this preprint.







29.05.17

S.Bardyla

Detecting Hclosed semigroups
A semigroup S is defined to be Hclosed if it is closed in each Hausdorff topological semigroup containing S as a discrete subsemigroup.
We shall try to characterize Hclosed semigroups in some classes of semigroups (completely simple, completely 0simple, completely regular, etc).







20.03.17

T.Banakh

On rulers and difference bases in finite groups
We discuss the recent progress on the (open) problem of determining the difference weight Δ[G] of a finite group G,
which is defined as the smallest cardinality of a subset B in G such that BB^{1}=G. It is clear that Δ[G]^{2}>G.
Using known information on rulers we shall prove that each cyclic group G of cardinality
G>2×10^{10} has difference weight Δ[G]^{2}<4G/3.







20.03.17

T.Banakh

On rulers and difference bases in finite groups
We discuss the recent progress on the (open) problem of determining the difference weight Δ[G] of a finite group G,
which is defined as the smallest cardinality of a subset B in G such that BB^{1}=G. It is clear that Δ[G]^{2}>G.
Using known information on rulers we shall prove that each cyclic group G of cardinality
G>2×10^{10} has difference weight Δ[G]^{2}<4G/3.







13.03.17

I.Pozdniakova

On semigroups of partial injective transformations of some partially ordered sets
We describe the Green relations and the congruence lattice of the semigroups of
partial injective transformations of some partially ordered sets.







27.02.17

S.Bardyla

Нclosed topological semigroups and semilattices
We discuss principal results of the Ph.D. Thesis (written under supervision of O.Gutik), which are related to:
 topologization of the αbicyclic monoid,
 embeddings of polycyclic monoids into compactlike topological semigroups, and
 Hclosedness of topological semilattices.







20.02.17

All

Divertisement
The active participants of the seminar will discuss some open problems and new results obtained during Winter Holydays.







January

All

Winter Holydays







26.12.16

B.Bokalo

Some open problems related to the weak continuity
We shall discuss some new results and open problems related to the weak continuity of functions.







05.12.16
12.12.16

M.Zarichnyi

Selfsimilar idempotent measures (I and II)
In the idempotent mathematics, the notion of idempotent measure
(Maslov measure) is a counterpart of the notion of probability measure. The aim
of the talk is to discuss the existence of an invariant idempotent measure for an
iterated function system on a complete metric space.
(This is a joint talk with N. Mazurenko).







28.11.16

T.Banakh

Separation Axioms in Quasitopological groups
We discuss Separations Axioms in quasitopological groups and construct an example of a regular quasitopological groups,
which is not functionally Hausdorff.







21.11.16

O.Ravsky

Strongly σmetrizable spaces are super σmetrizable
A topological space X is called strongly σmetrizable if X is the union of an increasing sequence
(X_{n})_{n∈ω}, of closed metrizable subspaces such that every convergence sequence in
X is contained in some X_{n}. If, in addition, every compact subset of X is contained in some
X_{n}, n∈ω, then X is called super σmetrizable.
Answering a question of V.K.Maslyuchenko and O.I.Filipchuk, we prove that a topological space is strongly σmetrizable
if and only if it is super σmetrizable.







14.11.16

T.Banakh

Strongly σmetrizable spaces are super σmetrizable
A topological space X is called strongly σmetrizable if X is the union of an increasing sequence
(X_{n})_{n∈ω}, of closed metrizable subspaces such that every convergence sequence in
X is contained in some X_{n}. If, in addition, every compact subset of X is contained in some
X_{n}, n∈ω, then X is called super σmetrizable.
Answering a question of V.K.Maslyuchenko and O.I.Filipchuk, we prove that a topological space is strongly σmetrizable
if and only if it is super σmetrizable.







07.11.16

Аспіранти

Звіти по наукову роботу за 2016 рік
Аспіранти кафедри (С.Бардила, М.Сімків, І.Титар) розкажуть про свої наукові досягнення за 2016 рік.







31.10.16

O.Karlova

Baire one functions depending on finitely many coordinates
Two questions from [V.Bykov, On Baire class one functions on a product space, Topol. Appl. 199 (2016) 5562] will be discussed. In particular, we will prove that
every Baire one function on a subspace of a countable perfectly normal product is the pointwise limit of a sequence of continuous functions, each depending on finitely many coordinates.
It is proved also that a lower semicontinuous function on a subspace of a countable perfectly normal product is the pointwise limit of an increasing sequence of continuous functions,
each depending on finitely many coordinates, if and only if the function has a minorant which depends on finitely many coordinates.







24.10.16

T.Banakh

On Haarnull and Haarmeager sets in Polish groups
We discuss interplay between (generically) Haarmeager and (generically) Haarnull sets in Polish groups.







10.10.16

All

Divertissement
The active participants of the seminar will discuss some open problems and possible ways of their solutions.







03.10.16

Ostap Chervak

Color guessing on graphs
A variant of a classic gnome and hats problem will be discussed. For an oriented graph let us consider the following guessing game.
A gnome is sitting on each vertex of an oriented graph and tries to guess its own hat color by looking on the colors of its neighbours.
By the colorguess number cg(G) denote the largest number of colors k such that gnomes have a strategy where at least one of them guesses its hat color correctly.
It is known that cg( K_{k} )=k. B.Bosek, J.Grytchuk and others asked if cg(G) is bounded if G is a bipartite graph or a simple directed graph. It will be proved that cg(K_{k,exp(k +3 log(k))})>k and there exist a simple directed graph on Cexp(k+3log(k)) vertices with cg(G)>k.







26.09.16

Ostap Chervak

On Ramsey trees
A notion of Ramsey trees will be introduced. They will offer a useful framework for various Ramseytype problems
including the Ramsey multiplicity problem and the Erdős cliqueindependent set problem. The connection to
Conlon's bound for Ramsey multiplicity constant will be discussed as well.







5.09.16

Oleg Pikhurko

Measurable circle squaring
In 1990 Laczkovich proved that one can split a disk into finitely many
parts and move them to form a partition of a square, thus solving the
longstanding Tarski's circle squaring problem. I will discuss our
result with Andras Mathe and Lukasz Grabowski that, additionally,
one can require that all parts are Lebesgue measurable and have the
property of Baire.





