Productivity of Coreflective Subcategories of Semitopological Groups

Abstract

The present paper generalizes to semitopological and quasitopological groups some results achieved by Horst Herrlich and the second author for topological groups. The results concern preserving products in coreflective subcategories.

Unlike in paratopological or topological groups, there are non-finitely productive bicoreflective subcategories of quasitopological groups. We desctribe bicoreflective subcategories of semitopological groups that are either finitely productive or productive ortheir productivity number is submeasurable.

Keywords

• semitopological groups
• quasitopological groups
• coreflective subclasses
• productivity
• submeasurable cardinal