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arXiv · 0811.4276

Embedding the bicyclic semigroup into countably compact topological semigroups

Taras Banakh·Svetlana Dimitrova·Oleg Gutik
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Abstract

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonov semigroup containing a copy of C(p,q).

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Taras Banakh, Svetlana Dimitrova, Oleg Gutik. 2008-11-26. Embedding the bicyclic semigroup into countably compact topological semigroups. https://doi.org/10.1016/j.topol.2010.08.020

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