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 Scientific Seminar: Topological Algebra Founded by Igor Guran & Oleg Gutik in 2007
 Speaker: Serhii Bardyla (Kurt Gödel Research Center, University of Vienna) Talk: Closed subspaces of compact-like spaces When & where: July 19, 2019, at 1505 at Room 149à Abstract: We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a closed subspace into an H-closed topological space. However, the semigroup of $\omega{\times\omega}$-matrix units cannot be embedded into a topological semigroup which is an H-closed 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, 2803-2814 (doi: 10.1016/j.topol.2010.08.020)]. This is joint work with A. Ravsky.

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