Geodesic
A Categorical Property of the Stone--\v Cech Compactification
Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 132-140.

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We study some categorical properties of the functor $O_\beta$ of weakly additive functionals acting in the category Tych of the Tychonoff spaces and their continuous mappings. We show that $O_\beta$ preserves the weight of infinite-dimensional Tychonoff spaces, the singleton, and the empty set, and that $O_\beta$ is monomorphic and continuous in the sense of T. Banakh, takes every perfect mapping to an epimorphism, and preserves intersections of functionally closed sets in a Tychonoff space. 
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R. B. Beshimov. A Categorical Property of the Stone--\v Cech  Compactification. Matematičeskie trudy, Tome 10 (2007) no. 1, pp. 132-140. http://geodesic.mathdoc.fr/item/MT_2007_10_1_a4/

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