On the functor properties of the $\Omega$-saturation of a topological $T_1$-space

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 $X\stackrel{f}{\longrightarrow}Y$ which admit a continuous extension $s_\Delta X\stackrel{\tilde f}{\longrightarrow}s_\Delta Y$, 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.