

September 8, 2011
 O.Ravsky

 Наївна спроба отримати алгебраїчну характеризацію
напівгруп ендоморфізмів класу F моноунарних алгебр: структура
напівгруп ендоморфізмів моноунарних алгебр класу F (початок)
 The reporter will be discussed on the topics which are annonced in
the title of report.



September 15, 2011,
September 22, 2011,
September 29, 2011
 O. Ravsky

 Моноунарні алгебри: хто вони?
 Будуть наведені різноманітні приклади моноунарних алгебр з
різних галузей математики, зокрема у Проблемі 3n+1, конвеєвскій грі "Житття" та фракталах.
По останнім двом прикладам планується КІНО



October 6, 2011,
October 13, 2011,
October 20, 2011
 O. Ravsky

 The product of a nonempty family of pseudocompact
paratopological groups is pseudocompact
 Will be proved the statement which is announced in the title.



Februaary 15, 2012
 O. Ravsky


A specific example of a locally compact cancellative semigroup S which cannot be a subsemigroup
of a paratopological group.

Answering a next question of I. Guran we construct a locally compact Polish cancellative
abelian semigroup S such that all shifts on S are quasiopen (that is, int (a+U) is nonempty for
each element a\in S and each nonempty open subset U of S), but S cannot be a subsemigroup of a
paratopological group.



Februaary 22, 2012
 O. Ravsky


Each discrete subgroup of $S_\omega(X)$ is finite.

Let $X$ be an infinite set and $S_\omega(X)$ be the group of all bijections of $X$ with finite supporter,
endowed with the topology of the pointwise convergence. Inspired by the talk with I. Guran, we show that
each discrete subgroup of $S_\omega(X)$ is finite.



Februaary 29, 2012,
March 7, 2012,
March 14, 2012,
March 21, 2012,
March 28, 2012,
April 4, 2012
 O.
Gutik


On monoids of injective partial cofinite selfmaps.

We discuss on the semigroup $\mathscr{I}^{\mathrm{cf}}_\lambda$ of
injective partial cofinite selfmaps of infinite cardinal $\lambda$.
We show that $\mathscr{I}^{\mathrm{cf}}_\lambda$ is a bisimple
inverse semigroup and for every nonempty chain $L$ in
$E(\mathscr{I}^{\mathrm{cf}}_\lambda)$ there exists an inverse
subsemigroup $S$ of $\mathscr{I}^{\mathrm{cf}}_\lambda$ such that
$S$ is isomorphic to the bicyclic semigroup and $L\subseteq E(S)$,
we describe the Green relations on
$\mathscr{I}^{\mathrm{cf}}_\lambda$ and we prove that every
nontrivial congruence on $\mathscr{I}^{\mathrm{cf}}_\lambda$ is a
group congruence. We also prove that every Hausdorff locally compact
topology $\tau$ on $\mathscr{I}^{\mathrm{cf}}_\lambda$ such that
$(\mathscr{I}^{\mathrm{cf}}_\lambda,\tau)$ is a semitopological
semigroup, is discrete and we describe the closure of the discrete
semigroup $\mathscr{I}^{\mathrm{cf}}_\lambda$ in a topological
semigroup. Finally, we show that the (discrete) semigroup
$\mathscr{I}^{\mathrm{cf}}_\lambda$ cannot embed into a compactlike
topological semigroup for any infinite cardinal $\lambda$, and we
construct two nondiscrete Hausdorff topologies which turn
$\mathscr{I}^{\mathrm{cf}}_\lambda$ into a topological inverse
semigroup.



Agust 6, 2012,
Agust 8, 2012

Kateryna Pavlyk (University of Tartu, Estonia)


Pseudocompact topological Brandt $\lambda^0$extensions of semitopological semigroups

We introduce pseudocompact (resp., countably compact, sequentially compact, compact) topological Brandt
$\lambda^0$extensions of pseudocompact (resp., countably compact, sequentially compact, compact) semitopological
semigroups in the class of semitopological semigroups and establish the structure of such extensions.


