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.
@article{TIMB_2023_31_1_a1,
author = {A. S. Biadrytski},
title = {On the functor properties of the $\Omega$-saturation of a topological $T_1$-space},
journal = {Trudy Instituta matematiki},
pages = {6--13},
publisher = {mathdoc},
volume = {31},
number = {1},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMB_2023_31_1_a1/}
}
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/