Metrizability of Clifford topological semigroups

Taras Banakh, Oleg Gutik, Oles Potiatynyk +1

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…