33 citations · 241 across the 65 of their papers we have counts for
16 papers · 1 filter
A note on feebly compact semitopological symmetric inverse semigroups of a bounded finite rank
Oleg Gutik
We study feebly compact shift-continuous -topologies on the symmetric inverse semigroup of finite transformations of the rank . It is proved tha…
On the monoid of cofinite partial isometries of with a bounded finite noise
Oleg Gutik, Pavlo Khylynskyi
In the paper we study algebraic properties of the monoid of cofinite partial isometries of the set of positive integers $\mathbb…
The Lawson number of a semitopological semilattice
Taras Banakh, Serhii Bardyla, Oleg Gutik
For a Hausdorff topologized semilattice its is the smallest cardinal such that for any distinct points there exists a family $\mat…
On the lattice of weak topologies on the bicyclic monoid with adjoined zero
Serhii Bardyla, Oleg Gutik
A Hausdorff topology on the bicyclic monoid with adjoined zero is called {\em weak} if it is contained in the coarsest inverse semigroup topology on $\mathcal{C…
On feebly compact semitopological semilattice
Oleg Gutik, Oleksandra Sobol
We study feebly compact shift-continous topologies on the semilattice . It is proved that such -topology is sequentially pracompact if and only if i…
On old and new classes of feebly compact spaces
Oleg Gutik, Alex Ravsky
We introduce three new classes of pracompact spaces, consider their basic properties and relations with other compact-like spaces.
On feebly compact shift-continuous topologies on the semilattice
Oleg Gutik, Oleksandra Sobol
We study feebly compact topologies on the semilattice such that is a semitopological semilattice and prove that for any shi…
On feebly compact topologies on the semilattice
Oleg Gutik, Oleksandra Sobol
We study feebly compact topologies on the semilattice such that is a semitopological semilattice. All compact semilattice $…
-closed quasitopological groups
Serhiy Bardyla, Oleg Gutik, Alex Ravsky
An -closed quasitopological group is a Hausdorff quasitopological group which is contained in each Hausdorff quasitopological group as a closed subspace. We obtained a sufficien…
On -complete topological semilattices
S. Bardyla, O. Gutik
In the paper we describe the structure of -completions and -completions of the discrete semilattices and . We give…
Topological monoids of monotone injective partial selfmaps of with cofinite domain and image
Oleg Gutik, Dušan Repovš
In this paper we study the semigroup of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}…
Metrizability of Clifford topological semigroups
Taras Banakh, Oleg Gutik, Oles Potiatynyk +1
We prove that a topological Clifford semigroup is metrizable if and only if is an -space and the set of idempotents of is a metrizable -set…
Embedding the bicyclic semigroup into countably compact topological semigroups
Taras Banakh, Svetlana Dimitrova, Oleg Gutik
We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that each topological semigroup S with pseudoco…
The Rees-Suschkewitsch Theorem for simple topological semigroups
Taras Banakh, Svetlana Dimitrova, Oleg Gutik
We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich f…
The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups
Oleg V. Gutik, Dušan Pagon, Dušan Repovš
In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup in is a (closed) topological…
On chains in -closed topological pospaces
Oleg V. Gutik, Dušan Pagon, Dušan Repovš
We study chains in an -closed topological partially ordered space. We give sufficient conditions for a maximal chain in an -closed topological partially ordered space suc…