Closed subsets of compact-like topological spaces

Autor:	Serhii Bardyla, Alex Ravsky
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	pseudocompact space h-closed space semigroup of matrix units bicyclic monoid Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Applied General Topology, Vol 21, Iss 2, Pp 201-214 (2020)
Druh dokumentu:	article
ISSN:	1576-9402 1989-4147
DOI:	10.4995/agt.2020.12258
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/48c5fbd1b8c345e5bcf0e4f95fce25a8 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF