Some concepts of topology and questions in topological algebra

Abstract

AbstractThis paper has features of mixed nature. It contains new results, in particular, on semitopological groups. We also pose some problems, introduce new definitions and describe in details certain techniques we need below, providing the proofs of not so well-known theorems for the sake of completeness. Hence, this article can be treated also as a kind of a short survey.Mathematics Subject Classification (2020): 54A2554D2054D4054E18Key words: Semitopological grouphomogeneous spacep-spaceLindelöf p-spaces-spaceremaindercountably compactσ-compactgroup number