On paracompact spaces and projectively inductively closed functors


  • T.F. Zhuraev Moscow State University




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


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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Author Biography

T.F. Zhuraev, 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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How to Cite

T. Zhuraev, “On paracompact spaces and projectively inductively closed functors”, Appl. Gen. Topol., vol. 3, no. 1, pp. 33–44, Apr. 2002.