Embedding the bicyclic semigroup into countably compact topological semigroups
General Topology
2011-10-11 v3 Group Theory
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).
Cite
@article{arxiv.0811.4276,
title = {Embedding the bicyclic semigroup into countably compact topological semigroups},
author = {Taras Banakh and Svetlana Dimitrova and Oleg Gutik},
journal= {arXiv preprint arXiv:0811.4276},
year = {2011}
}
Comments
14 pages