Some concepts of topology and questions in topological algebra

Abstract

This 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):

• 54A25
• 54D20
• 54D40
• 54E18

Key words:

• Semitopological group
• homogeneous space
• p-space
• Lindelöf p-space
• s-space
• remainder
• countably compact
• σ-compact
• group number