Pseudocompact and precompact topological subsemigroups of topological groups

Abstract

It is known that every pseudocompact topological group is precompact, we extend this result to a class of subsemigroup of topological groups. Then we use this results to prove that cancellative locally compact countably compact topological semigroups with open shifts are topological groups and to give a sufficient condition under which a locally compact monothetic topological semigroup is a compact topological group.

Keywords

• topological semigroup
• topological group
• pseudocompact space
• precompact set
• feebly compact space