On paracompact spaces and projectively inductively closed functors

Abstract

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.

Keywords

• Stratifiable space
• Paracompact σ-spaces
• Paracompact Σ-spaces
• Paracompact p-space
• Projectively inductively closed functor