Embedding the bicyclic semigroup into countably compact topological semigroups

Details Embedding the bicyclic semigroup into countably compact topological semigroups Embedding the bicyclic semigroup into countably compact topological semigroups

2008-11-26

arxiv.org/abs/0811.4276v3

Topology Appl. Vol.157, No.18 (2010) 2803-2814

Mathematics

General Topology

14 pages

Scientific paper

10.1016/j.topol.2010.08.020

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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