This article is cited in 1 paper

Geometry and Topology

Functor properties of the $\Omega$-saturation of a topological space

A. S. Biadrytski, V. L. Timokhovich

aBelarusian State University, 4 Niezalieznasci Avenue, Minsk 220030, Belarus

Abstract: Herein, we consider the $\Omega$-saturations of a topological space $X$, which are canonically embedded in the Wallman extension $\omega X$ and are a weakening of the concept of the countably-compactification in the Morita sense. We find necessary and sufficient conditions of the continious extension of a map $X \xrightarrow{f} Y$ to $\Omega$-saturations of the spaces $X$ and $Y$, as well as sufficiently wide categories on which the covariant functors arising in this case are defined.

Keywords: saturation of a topological space; countably-compactification in the Morita sense; Wallman compactification.

UDC: 515.12

Received: 18.12.2021
Revised: 09.11.2022
Accepted: 09.03.2023

DOI: 10.33581/2520-6508-2023-1-31-37

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