SOME PROPERTIES OF COVARIANT FUNCTORS ON THE CATEGORY Comp

Abstract

In this note, we consider covariant functors in the categories of Comp−compact spaces, Metrmetrizable spaces, S -stratifiable spaces, −  spaces, paracompact p -spaces, and continuous self-maps. It is proved that functors with finite supports acting in certain categories preserve finite-dimensional spaces and weakly countable spaces. Closed functors with finite support are defined and it is proved that closed functors preserve the class of S -spaces.