A Categorical Property of the Stone–Čech Compactification

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.