On a Covariant Functor v in the Category R - of Compact Tychonov Spaces and their Continuous Mappings into Itself

Abstract

This note defines a covariant functor V: ТуchТусh acting on the category of Tychonov spaces and continuous mappings into itself. Studying the topological and categorical properties of this functor V, it is shown that the functor V is a normal functor in the category R - of compact spaces and continuous mappings into itself, which is a subcategory of Тусh . It is proved that the functor V: ТуchТусh is an open functor, in the considered category R - of compact spaces and continuous mappings into yourself.