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 Raı̌kov-complete. Also we present examples of non-compact quasitopological groups whose topological spaces are H-closed.