Bardyla, SerhiiRavsky, Alex2020-10-072020-10-072020-10-011576-9402https://riunet.upv.es/handle/10251/151360[EN] 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 ofcountably 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.Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)Pseudocompact spaceH-closed spaceSemigroup of matrix unitsBicyclic monoidArtículo10.4995/agt.2020.12258Abierto1989-4147