Closed subsets of compact-like topological spaces

Serhii Bardyla; Alex Ravsky

doi:10.4995/agt.2020.12258

Authors

Serhii Bardyla University of Vienna https://orcid.org/0000-0003-2266-2024
Alex Ravsky National Academy of Sciences

DOI:

https://doi.org/10.4995/agt.2020.12258

Keywords:

pseudocompact space, H-closed space, semigroup of matrix units, bicyclic monoid

Abstract

We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We show that each Hausdorff topological space is a closed subspace of some Hausdorff ω-bounded pracompact topological space and describe open dense subspaces of
countably pracompact topological spaces. We construct a pseudocompact topological semigroup which contains the bicyclic monoid as a closed subsemigroup. This example provides an affirmative answer to a question posed by Banakh, Dimitrova, and Gutik in [4]. Also, we show that the semigroup of ω×ω-matrix units cannot be embedded into a Hausdorff topological semigroup whose space is weakly H-closed.

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Author Biographies

Serhii Bardyla, University of Vienna

Institute of Mathematics

Alex Ravsky, National Academy of Sciences

Pidstryhach Institute for Applied Problems of Mechanics and Mathematics

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