Embedding the bicyclic semigroup into countably compact topological semigroups

By Taras O. Banakh, Svetlana Dimitrova, Oleg Gutik. 2008

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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 a 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) Tychonoff semigroup containing a copy of C ( p , q ) .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7736635793af828e39c99fe0fedfd6b6dc4eaf3f