TY - JOUR
AU - Bardyla, Serhii
AU - Ravsky, Alex
PY - 2020/10/01
Y2 - 2023/03/26
TI - Closed subsets of compact-like topological spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 21
IS - 2
SE -
DO - 10.4995/agt.2020.12258
UR - https://polipapers.upv.es/index.php/AGT/article/view/12258
SP - 201-214
AB - <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>
ER -