18 citations · 121 across the 42 of their papers we have counts for
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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…
A metrizable Lawson semitopological semilattice with non-closed partial order
Taras Banakh, Serhii Bardyla, Alex Ravsky
We construct a metrizable Lawson semitopological semilattice whose partial order is not closed in . This resolves a problem posed…
Closed subsets of compact-like topological spaces
Serhii Bardyla, Alex Ravsky
We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a clo…
Embeddings into countably compact Hausdorff spaces
Taras Banakh, Serhii Bardyla, Alex Ravsky
In this paper we consider the problem of characterization of topological spaces that embed into countably compact Hausdorff spaces. We study the separation axioms of subspaces of c…
Positive answers to Koch's problem in special cases
Taras Banakh, Serhii Bardyla, Igor Guran +2
A topological semigroup is monothetic provided it contains a dense cyclic subsemigroup. The Koch problem asks whether every locally compact monothetic monoid is compact. This probl…