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

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.

A functor IS in the Category Compact Hausdorff Spaces

We construct a space of normed, homogeneous and max-plus-semiadditive functionals and we give its description. Further we establish that the construction of taking of a space of normed, homogeneous and max-plus-semiadditive functionals, forms a normal functor acting in the category of Hausdorff compact spaces and their continuous maps.

On paracompact spaces and projectively inductively closed functors

<p>In this paper we introduce a notion of projectively inductively closed functor (p.i.c.-functor). We give sufficient conditions for a functor to be a p.i.c.-functor. In particular, any finitary normal functor is a p.i.c.-functor. We prove that every preserving weight p.i.c.- functor of a finite degree preserves the class of stratifiable spaces and the class of paracompact -spaces. The same is true (even if we omit a preservation of weight) for paracompact -spaces and paracompact p-spaces.</p>