Geodesic
On the functor properties of the $\Omega$-saturation of a topological $T_1$-space
Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 6-13.

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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. 
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A. S. Biadrytski. On the functor properties of the $\Omega$-saturation of a topological $T_1$-space. Trudy Instituta matematiki, Tome 31 (2023) no. 1, pp. 6-13. http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a1/

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