Commutative Topological Semigroups Embedded into Topological Abelian Groups

Abstract

In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative topological monoid with open shifts. Finally, we use these results to give sufficient conditions on a commutative topological semigroup that guarantee it to have countable cellularity.

Keywords

• cancellative topological semigroup
• cellularity
• <i>σ</i>-compact space
• feebly compact space