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Embedding the bicyclic semigroup into countably compact topological semigroups |
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| Authors: | Taras Banakh Svetlana Dimitrova |
| Affiliation: | a Department of Mathematics, Ivan Franko National University of Lviv, Universytetska 1, Lviv, Ukraine b Instytut Matematyki, Uniwersytet Humanistyczno-Przyrodniczy Jana Kochanowskiego w Kielcach, ?wi?tokrzyska 15, Kielce, Poland c National Technical University “Kharkiv Polytechnical Institute”, Frunze 21, Kharkiv, 61002, Ukraine |
| 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). |
| Keywords: | Topological semigroup Semitopological semigroup Bicyclic semigroup Embedding Extension Semigroup compactification |
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