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...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 245; no. 3; pp. 382 - 389
Main Authors Ayupov, Sh. A., Zhuraev, T. F.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.03.2020
Springer
Springer Nature B.V
Subjects
Mathematics
Mathematics and Statistics
Monte Carlo simulation
Topology
sigma inductively closed functors
54B30
54B15
54B35
probability measure
54C05
Dugundji compactum
54C15
functor
Dirac measure
space
54O30
soft mapping
inductively closed functor
54C60
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-020-04700-9

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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 σ -p.i.c. functor that preserves soft mappings and various types of topological spaces.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04700-9