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Scientific Seminar:
Topological Algebra

Speaker: 
Serhii Bardyla (Kurt Gödel Research Center, University of Vienna)

Talk: 
Closed subspaces of compactlike spaces 
When & where:  July 19, 2019, at 15^{05 } at Room 149^{à} 
Abstract: 
We investigate closed subsets (subsemigroups, resp.) of compactlike topological spaces
(semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a closed
subspace into an Hclosed topological space. However, the semigroup of
$\omega{\times\omega}$matrix units cannot be embedded into a topological semigroup which is an Hclosed
topological space. We give sufficient conditions for closed embeddability of a topological space into countably pracompact topological spaces. Also, we construct a pseudocompact topological semigroup which contains the
bicyclic monoid as a closed subsemigroup, providing a positive solution of a problem posed by Banakh,
Dimitrova, and Gutik [T. Banakh, S. Dimitrova, and O. Gutik, Embedding the bicyclic semigroup into countably compact topological
semigroups, Topology Appl. 157 (2010), no. 18, 28032814
(doi: 10.1016/j.topol.2010.08.020)].
