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On pseudobounded and premeager paratopological groups
Taras Banakh, Alex Ravsky
Let be a paratopological group. Following F. Lin and S. Lin, we say that the group is pseudobounded, if for any neighborhood of the identity of , there exists a natu…
Suitable sets for paratopological groups
Fucai Lin, Alex Ravsky, Tingting Shi
A paratopological group has a {\it suitable set} . The latter means that is a discrete subspace of , is closed, and the subgroup of $…
A countably compact topological group with the non-countably pracompact square
Serhii Bardyla, Alex Ravsky, Lyubomyr Zdomskyy
Under Martin's Axiom we construct a Boolean countably compact topological group whose square is not countably pracompact.
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…
A note on compact-like semitopological groups
Alex Ravsky
The note contains a few results related to separation axioms and automatic continuity of operations in compact-like semitopological groups. In particular, is presented a semiregula…
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…