On paracompact spaces and projectively inductively closed functors

T.F. Zhuraev


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.


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

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1. On Projectively Inductively Closed Subfunctors of the Functor P of Probability Measures
Sh. A. Ayupov, T. F. Zhuraev
Journal of Mathematical Sciences  vol: 245  issue: 3  first page: 382  year: 2020  
doi: 10.1007/s10958-020-04700-9

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