Metrizability of Clifford topological semigroups

Abstract

We prove that a topological Clifford semigroup $S$ is metrizable if and only if $S$ is an $M$-space and the set $E=\{e\in S:ee=e\}$ of idempotents of $S$ is a metrizable $G_{\delta }$-set in $S$. The same metrization criterion holds also for any countably compact Clifford topological semigroup $S$.

4 pages

References in corpus (1)

• The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

Cited by in corpus (1)

• Topological embeddings into transformation monoids