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On projectively inductively closed subfunctors of the functor \(P\) of probability measures. (English. Russian original) Zbl 1448.54005

J. Math. Sci., New York 245, No. 3, 382-389 (2020); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 144, 88-95 (2018).
Summary: 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 \(\sigma \)-p.i.c. functor that preserves soft mappings and various types of topological spaces.

MSC:

54B30 Categorical methods in general topology
54B35 Spectra in general topology
54C05 Continuous maps
54C15 Retraction
54C60 Set-valued maps in general topology
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References:

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