Metrizability of Clifford topological semigroups

Details Metrizability of Clifford topological semigroups Metrizability of Clifford topological semigroups

2011-05-13

arxiv.org/abs/1105.2806v2

Mathematics

General Topology

4 pages

Scientific paper

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 $S$.

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