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 in | Journal of mathematical sciences (New York, N.Y.) Vol. 245; no. 3; pp. 382 - 389 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.03.2020
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1072-3374 1573-8795 |
| DOI | 10.1007/s10958-020-04700-9 |
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| Abstract | 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. |
|---|---|
| AbstractList | In this paper, we examine topological and dimensional properties of metric, Tychonoff, and compact C-spaces under the action of the covariant subfunctor Pf 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 Pf of the functor P of probability measures and show that this functor Pf is an open a-p.i.c. functor that preserves soft mappings and various types of topological spaces. Keywords and phrases: functor, probability measure, Dirac measure, soft mapping, C-space, inductively closed functor, sigma inductively closed functors, Dugundji compactum. AMS Subject Classification: 54B15, 54B30, 54B35, 54C05, 54C15, 54C60, 54O30 In this paper, we examine topological and dimensional properties of metric, Tychonoff, and compact C-spaces under the action of the covariant subfunctor Pf 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 Pf of the functor P of probability measures and show that this functor Pf is an open a-p.i.c. functor that preserves soft mappings and various types of topological spaces. In this paper, we examine topological and dimensional properties of metric, Tychonoff, and compact C-spaces under the action of the covariant subfunctor Pf 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 Pf of the functor P of probability measures and show that this functor Pf is an open σ-p.i.c. functor that preserves soft mappings and various types of topological spaces. 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. |
| Audience | Academic |
| Author | Ayupov, Sh. A. Zhuraev, T. F. |
| Author_xml | – sequence: 1 givenname: Sh. A. surname: Ayupov fullname: Ayupov, Sh. A. email: sh_ayupov@mail.ru organization: Uzbekistan Academy of Sciences, V. I. Romanovskiy Institute of Mathematics – sequence: 2 givenname: T. F. surname: Zhuraev fullname: Zhuraev, T. F. organization: Tashkent State Pedagogical University named after Nizami |
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| Keywords | 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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| References | ZhuraevTFOn paracompact spaces, projectively inductively closed functors, and dimensionMath. Aterna2015511751891931250 FedorchukVitalii VProbability measures in topologyRussian Mathematical Surveys19914614593110903610.1070/RM1991v046n01ABEH002722 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). T. A. Chapman, Lectures on Hilbert Cube Manifolds, Am. Math. Soc., Providence, Rhose island (1976). KleeVSome topological properties of convex setsTrans. Am. Math.199578130456938810.1090/S0002-9947-1955-0069388-5 FedorchukVitalii VWeakly infinite-dimensional spacesRussian Mathematical Surveys2007622323374235236610.1070/RM2007v062n02ABEH004397 KellerOHDie Homeomorphie der kompakten konvexen Mengen im Hilbertschen RaumMath. Ann.19311051748758151274010.1007/BF01455844 ShchepinE VFunctors and uncountable powers of compactaRussian Mathematical Surveys198136317110.1070/RM1981v036n03ABEH004247 UspenskyVVTopological groups and Dugunji compactaMat. Sb.1989180810921118 ZhuraevTFOn projectively quotient functorsComment. Math. Univ. Carolinae200142356157318602451053.54019 ZhuraevTFOn paracompact spaces and projectively inductively closed functorsGen. Topol. Appl.2002313344193125010.4995/agt.2002.2110 ZhuraevTFOn dimension and p.i.c. functorsMath. Aterna201446577596 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. T. F. Zhuraev, Some Geometric Properties of the Functor of Probability Measures and Its Subfunctors [in Russian], Ph.D. Thesis (1989). TF Zhuraev (4700_CR12) 2002; 3 4700_CR9 TF Zhuraev (4700_CR14) 2015; 5 V Klee (4700_CR6) 1995; 78 4700_CR2 4700_CR1 TF Zhuraev (4700_CR13) 2014; 4 VV Uspensky (4700_CR8) 1989; 180 Vitalii V Fedorchuk (4700_CR3) 1991; 46 OH Keller (4700_CR5) 1931; 105 TF Zhuraev (4700_CR11) 2001; 42 E V Shchepin (4700_CR7) 1981; 36 Vitalii V Fedorchuk (4700_CR4) 2007; 62 4700_CR10 |
| References_xml | – reference: KellerOHDie Homeomorphie der kompakten konvexen Mengen im Hilbertschen RaumMath. Ann.19311051748758151274010.1007/BF01455844 – reference: ShchepinE VFunctors and uncountable powers of compactaRussian Mathematical Surveys198136317110.1070/RM1981v036n03ABEH004247 – reference: T. F. Zhuraev, Some Geometric Properties of the Functor of Probability Measures and Its Subfunctors [in Russian], Ph.D. Thesis (1989). – reference: FedorchukVitalii VProbability measures in topologyRussian Mathematical Surveys19914614593110903610.1070/RM1991v046n01ABEH002722 – reference: 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). – reference: 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. – reference: FedorchukVitalii VWeakly infinite-dimensional spacesRussian Mathematical Surveys2007622323374235236610.1070/RM2007v062n02ABEH004397 – reference: KleeVSome topological properties of convex setsTrans. Am. Math.199578130456938810.1090/S0002-9947-1955-0069388-5 – reference: T. A. Chapman, Lectures on Hilbert Cube Manifolds, Am. Math. Soc., Providence, Rhose island (1976). – reference: ZhuraevTFOn paracompact spaces and projectively inductively closed functorsGen. Topol. Appl.2002313344193125010.4995/agt.2002.2110 – reference: UspenskyVVTopological groups and Dugunji compactaMat. Sb.1989180810921118 – reference: ZhuraevTFOn projectively quotient functorsComment. Math. Univ. Carolinae200142356157318602451053.54019 – reference: ZhuraevTFOn dimension and p.i.c. functorsMath. Aterna201446577596 – reference: ZhuraevTFOn paracompact spaces, projectively inductively closed functors, and dimensionMath. Aterna2015511751891931250 – volume: 5 start-page: 175 issue: 1 year: 2015 ident: 4700_CR14 publication-title: Math. Aterna – volume: 78 start-page: 30 issue: 1 year: 1995 ident: 4700_CR6 publication-title: Trans. Am. Math. doi: 10.1090/S0002-9947-1955-0069388-5 – ident: 4700_CR9 – volume: 180 start-page: 1092 issue: 8 year: 1989 ident: 4700_CR8 publication-title: Mat. Sb. – volume: 3 start-page: 33 issue: 1 year: 2002 ident: 4700_CR12 publication-title: Gen. Topol. Appl. doi: 10.4995/agt.2002.2110 – ident: 4700_CR2 doi: 10.1090/cbms/028 – volume: 105 start-page: 748 issue: 1 year: 1931 ident: 4700_CR5 publication-title: Math. Ann. doi: 10.1007/BF01455844 – volume: 36 start-page: 1 issue: 3 year: 1981 ident: 4700_CR7 publication-title: Russian Mathematical Surveys doi: 10.1070/RM1981v036n03ABEH004247 – ident: 4700_CR1 – ident: 4700_CR10 – volume: 42 start-page: 561 issue: 3 year: 2001 ident: 4700_CR11 publication-title: Comment. Math. Univ. Carolinae – volume: 62 start-page: 323 issue: 2 year: 2007 ident: 4700_CR4 publication-title: Russian Mathematical Surveys doi: 10.1070/RM2007v062n02ABEH004397 – volume: 46 start-page: 45 issue: 1 year: 1991 ident: 4700_CR3 publication-title: Russian Mathematical Surveys doi: 10.1070/RM1991v046n01ABEH002722 – volume: 4 start-page: 577 issue: 6 year: 2014 ident: 4700_CR13 publication-title: Math. Aterna |
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| Snippet | 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... In this paper, we examine topological and dimensional properties of metric, Tychonoff, and compact C-spaces under the action of the covariant subfunctor Pf of... |
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| Title | On Projectively Inductively Closed Subfunctors of the Functor P of Probability Measures |
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