On paracompact spaces and projectively inductively closed functors

T.F. Zhuraev

Russian Federation

Moscow State University

Department of General Topology and Geometry

Mechanics and Mathematics Faculty

Moscow State University

Vorob'evy Gory, Moscow, 119899 Russia

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Accepted: 2014-01-27

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Published: 2002-04-01

DOI: https://doi.org/10.4995/agt.2002.2110
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Keywords:

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

Supporting agencies:

This research was not funded

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.

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