On Projectively Inductively Closed Subfunctors of the Functor P of Probability Measures

In this paper, we examine topological and dimensional properties of metric, Tychonoff, and compact C -spaces under the action of the covariant subfunctor P f of the functor P of probability measures in the category of metric, compact, and paracompact spaces and continuous self-mappings. We consider geometric properties of spaces under the action of the subfunctor P f of the functor P of probability measures and show that this functor P f is an open σ -p.i.c. functor that preserves soft mappings and various types of topological spaces.