Functor properties of the Ω-saturation of a topological space - Biadrytski, Aliaksandr S.; Timokhovich, Vladimir L. (Journal of the Belarusian State University. Mathematics and Informatics, 2023)
Herein, we consider the Ω-saturations of a topological space X, which are canonically embedded in the Wallman extension ωX 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 to Ω-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