Ayupov, Sh. A.; Zhuraev, T. F. 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 Keywords:functor; probability measure; Dirac measure; soft mapping; \(C\)-space; inductively closed functor; sigma inductively closed functors; Dugundji compactum PDFBibTeX XMLCite \textit{Sh. A. Ayupov} and \textit{T. F. Zhuraev}, J. Math. Sci., New York 245, No. 3, 382--389 (2020; Zbl 1448.54005); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 144, 88--95 (2018) Full Text: DOI References: [1] Sh. A. Ayupov and T. F. Zhuraev, “Spaces and covariant functors of finite dgree,” in: Problems of Modern Topology and Its Applications [in Russian], Tashkent (2016), pp. 14-20. [2] T. A. Chapman, Lectures on Hilbert Cube Manifolds, Am. Math. Soc., Providence, Rhose island (1976). · Zbl 0347.57005 [3] Fedorchuk, Vitalii V., Probability measures in topology, Russian Mathematical Surveys, 46, 1, 45-93 (1991) · Zbl 0735.54033 [4] Fedorchuk, Vitalii V., Weakly infinite-dimensional spaces, Russian Mathematical Surveys, 62, 2, 323-374 (2007) · Zbl 1154.54022 [5] Keller, OH, Die Homeomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann., 105, 1, 748-758 (1931) · Zbl 0003.22401 [6] Klee, V., Some topological properties of convex sets, Trans. Am. Math., 78, 1, 30-45 (1995) · Zbl 0064.10505 [7] Shchepin, E. V., Functors and uncountable powers of compacta, Russian Mathematical Surveys, 36, 3, 1-71 (1981) · Zbl 0487.54011 [8] Uspensky, VV, Topological groups and Dugunji compacta, Mat. Sb., 180, 8, 1092-1118 (1989) [9] T. F. Zhuraev, Some Geometric Properties of Subfunctors of the Functor of Probability Measures [in Russian], deposited at the All-Union Institute for Scientific and Technical Information (VINITI), No. 4471 (1989). [10] T. F. Zhuraev, Some Geometric Properties of the Functor of Probability Measures and Its Subfunctors [in Russian], Ph.D. Thesis (1989). [11] Zhuraev, TF, On projectively quotient functors, Comment. Math. Univ. Carolinae, 42, 3, 561-573 (2001) · Zbl 1053.54019 [12] Zhuraev, TF, On paracompact spaces and projectively inductively closed functors, Gen. Topol. Appl., 3, 1, 33-44 (2002) · Zbl 1025.54007 [13] Zhuraev, TF, On dimension and p.i.c. functors, Math. Aterna, 4, 6, 577-596 (2014) [14] Zhuraev, TF, On paracompact spaces, projectively inductively closed functors, and dimension, Math. Aterna, 5, 1, 175-189 (2015) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.