The Rees-Suschkewitsch Theorem for simple topological semigroups

Details The Rees-Suschkewitsch Theorem for simple topological semigroups The Rees-Suschkewitsch Theorem for simple topological semigroups

2008-11-09

arxiv.org/abs/0811.1371v2

Mat. Stud., Vol.31, No.2 (2009) 211-218

Mathematics

General Topology

8 pages

Scientific paper

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is a topological paragroup if one of the following conditions is satisfied: (1) $S$ is completely simple and the maximal subgroups of $S$ are topological groups, (2) $S$ contains an idempotent and the square $S\times S$ is countably compact or pseudocompact, (3) $S$ is sequentially compact or each power of $S$ is countably compact. The last item generalizes an old Wallace's result saying that each simple compact topological semigroup is a topological paragroup.

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