Embedding the bicyclic semigroup into countably compact topological semigroups

作者：Banakh Taras^*; Dimitrova Svetlana; Gutik Oleg

来源：Topology and Its Applications, 2010, 157(18): 2803-2814.

DOI：10.1016/j.topol.2010.08.020

• Topological semigroup
• Semitopological semigroup
• Bicyclic semigroup
• Embedding
• Extension
• Semigroup compactification

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).

• 出版日期2010-12-1