Mathematica Eterna
Open Access

Abstract

On dimension and σ-p.i.c.-functors

Tursun F. Zhuraev

In this paper we introduce a notion of σ-p.i.c.-functor. We prove that the functor Pk of probabilities measures supported on ≤ k points is a σ - p.i.c.-functor and the logarithmic law for Lebesgue dimension takes place for Pk and paracompact p-spaces and stratifiable spaces. We consider also a problem of a preservation of the class of weakly countable-dimensional spaces by some σ-p.i.c - functors.