Closed subsets of compact-like topological spaces

Abstract

<p>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<br />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.</p>

Locations

• Applied General Topology - View - PDF
• arXiv (Cornell University) - View - PDF
• DOAJ (DOAJ: Directory of Open Access Journals) - View
• Repositorio Institucional de la Universitat Politècnica (Universitat Politècnica de València) - View - PDF