On paracompact spaces and projectively inductively closed functors
DOI:
https://doi.org/10.4995/agt.2002.2110Keywords:
Stratifiable space, Paracompact σ-spaces, Paracompact Σ-spaces, Paracompact p-space, Projectively inductively closed functorAbstract
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.
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