

October 8, 2009

I. Guran,
O. Gutik,
O. Ravsky


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



October 15, 2009,
October 22, 2009,
October 29, 2009

O. Gutik


Topological semigroups of cofinite
monotone bijective partial transformations of positive integers

We show that the semigroup
of partial cofinal
monotone bijective transformations of the set of positive integers has algebraic
properties similar to the bicyclic semigroup: it is bisimple and
all of its nontrivial group homomorphisms are either isomorphisms
or group homomorphisms. We also prove that every locally compact
topology on the semigroup
of partial cofinal
monotone bijective transformations of the set of positive integers S
such that S is a topological inverse semigroup is discrete and we describe the
closure of S in a topological semigroup.



November 12, 2009

A. Reiter


On Hclosed Clifford topological inverse semigroups

We show that an arbitrary Clifford topological inverse semigroup with an algebraic closed maximal subsemilattice and Hclosed maximal subgroups is Hclosed in the class of topological inverse semigroups.



November 19, 2009

O. Gutik


On Hclosed inverse semigroup topologies on the semigroup of finite partial bijections of a bounded finite rank

We show that the topological inverse semigroup of finite partial bijections of a bounded finite rank I_{λ}^{n} is Hclosed if and only if its band E(I_{λ}^{n}) is compact. Also we construct Hclosed semigroup topology on I_{λ}^{n} such that the band E(I_{λ}^{n}) is a discrete subspace of I_{λ}^{n}.



November 26, 2009,
December 24, 2009

O. Gutik


On chains in Hclosed topological pospaces

We study chains in an Hclosed topological partially ordered
space. We give sufficient conditions for a maximal chain L in an
Hclosed topological partially ordered space (Hclosed
topological semilattice) under which L contains a maximal
(minimal) element. We also give sufficient conditions for a
linearly ordered topological partially ordered space to be
Hclosed. We prove that a linearly ordered Hclosed
topological semilattice is an Hclosed topological pospace and
show that in general, this is not true. We construct an example of
an Hclosed topological pospace with a nonHclosed maximal
chain and give sufficient conditions under which a maximal chain
of an Hclosed topological pospace is an Hclosed topological
pospace.



February 18, 2010

I. Guran,
O. Gutik


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



February 25, 2010,
March 4, 2010,
March 11, 2010

I. Guran,


On a metrizability of cancellative topological semigroups

We discuss on a metrizability of cancellative topological semigroups.



March 18, 2010

I. Guran,


Koch Problem on monothetic topological semigroups

We give the sufficient conditions on a locally compact topological semigroup under which the Pontryagin Alternative holds.



March 25, 2010

O. Gutik


On a finite symmetric inverse semigroup of bounded rank

We describe all congruences on a finite symmetric inverse semigroup of bounded rank and show that it is algebraically hclosed in the
class in semitopological inverse semigroups with continuous inversion.



April 1, 2010

L. Zdomskyy


On maximal almost disjoint families

The talk will be devoted to different types of maximal almost disjoint families.
In particular, several constructions of strongly maximal almost
disjoint families of
functions will be presented.



April 8, 2010

O. Gutik


On compact topologies on a finite symmetric inverse semigrou of bounded rank

We describe all compact and countable compact Hausdorff topologies on a finite symmetric inverse semigroup of bounded rank I_{λ}^{n} such that I_{λ}^{n} is a semitopological semigroup.



April 29, 2010

I. Pastukhova


Continuously cancellative Clifford inverse topological semigroups.

We prove that a Clifform inverse topological semigroup S whose idempotent band E is a Usemilattice embeds into a compact Clifford topological inverse semigroup with zerodimensional band if and only if
 E embeds into a zerodimensional compact semilattice;
 the maximal subgroups H_{e} of S are totally bounded;
 S is continuously cancellative.
A Clifford topological inverse semigroup S is called continuously cancellative is for each point x in S and a neighborhood O(x) there are neighborhoods U(x) and O(e) of the idempotent e=xx^{1} such that a point y of S belongs to the neighborhood O(x) provided yy^{1} lies in O(e) and ye lies in U(x).




May 6, 2010

I. Chuchman


On a semigroup of almost monotone partial bijective transformations of positive intergers.

We discuss on algebraic properties of the semigroup of almost monotone partial bijective
transformations of positive intergers ant its topologizations as semitopological and topological semigroups.


