Embedding the bicyclic semigroup into countably compact topological semigroups
arXiv:0811.4276 · doi:10.1016/j.topol.2010.08.020
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).
14 pages