On the functor properties of the Ω-saturation of a topological T1-space

Abstract

For a topological $T_1$-space we consider a $\Omega$-saturation, which is canonically embedded in the Wallman extension $\omega X$. In a certain sense, this saturation is maximal with respect to inclusion among all saturations of this type. A class of maps $X \overset{f}{\longrightarrow} Y$ which admit a continuous extension $s_{\Delta}X \overset{\tilde{f}}{\longrightarrow} s_{\Delta} Y$, where $s_{\Delta}X$ and $s_{\Delta}Y$ are the $\Omega$-saturations (mentioned above) of the spaces $X$ and $Y$ respectively is found. It is shown that these maps, together with the class of topological $T_1$-spaces, form a category, and the construction of the $\Omega$-saturation considered in the paper defines a covariant functor from the indicated category into the category TOP of topological spaces and continuous maps.