$H$-closed quasitopological groups

Abstract

An $H$-closed quasitopological group is a Hausdorff quasitopological group which is contained in each Hausdorff quasitopological group as a closed subspace. We obtained a sufficient condition for a quasitopological group to be $H$-closed, which allowed us to solve a problem by Arhangel'skii and Choban and to show that a topological group $G$ is $H$-closed in the class of quasitopological groups if and only if $G$ is Ra\vıkov-complete. Also we present examples of non-compact quasitopological groups whose topological spaces are $H$-closed.

7 pages

References in corpus (1)

• On H-closed paratopological groups

Cited by in corpus (4)

• On a complete topological inverse polycyclic monoid
• Characterizing chain-compact and chain-finite topological semilattices
• Categorically closed topological groups
• Completeness and absolute $H$-closedness of topological semilattices