On the countably-compactifiability in the sense of Morita

  • Hleb O. Kukrak Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
  • Vladimir L. Timokhovich Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
DOI: https://doi.org/10.33581/2520-6508-2021-1-46-53

Abstract

We consider an extension Y of a topological space X that is canonically embedded in the Wallman extension ωX, in which any countably compact set closed in X is closed and such that any infinite set contained in X has a limit point in it. This extension is called saturation of the space X. We find a necessary and sufficient condition for the countable compactness of the space Y. Thus the problem of existence of countably-compactification in the sense of Morita of certain type is solved.

Author Biographies

Hleb O. Kukrak, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics); associate professor at the department of geometry, topology and mathematics teaching methodology, faculty of mechanics and mathematics

Vladimir L. Timokhovich, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics), docent; associate professor at the department of geometry, topology and mathematics teaching methodology, faculty of mechanics and mathematics

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Published
2021-04-12
Keywords: countably-compactification in the sense of Morita, Wallman compactification, saturation of topological space
How to Cite
Kukrak, H. O., & Timokhovich, V. L. (2021). On the countably-compactifiability in the sense of Morita. Journal of the Belarusian State University. Mathematics and Informatics, 1, 46-53. https://doi.org/10.33581/2520-6508-2021-1-46-53
Issue
No 1 (2021): Journal of the Belarusian State University. Mathematics and Informatics
Section
Geometry and Topology

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