A. A. Zaitov, “Geometrical and topological properties of a subspace $P_f(X)$ of probability measures”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 10, 28–37; Russian Math. (Iz. VUZ), 63:10 (2019), 24

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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 10, Pages 28–37
DOI: https://doi.org/10.26907/0021-3446-2019-10-28-37 (Mi ivm9504)

This article is cited in 13 scientific papers (total in 13 papers)

Geometrical and topological properties of a subspace

$P_f(X)$ of probability measures

A. A. Zaitov

Tashkent Instute of Architecture and Civil Engineering, 13 Navoi str., Tashkent, 100011 Uzbekistan

Full-text PDF (380 kB) Citations (13)

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DOI: https://doi.org/10.26907/0021-3446-2019-10-28-37

Abstract: We prove that for a compact

$X$ the space

$P_{f}(X)$ is an absolute neighbourhood retract if and only if

$X$ is an absolute neighbourhood retract. Futher, we demonstrate that a functor

$P_{f}$ preserves the property of a compact to be

$Q$ -manifold or Hilbert cube, preserves the propetry of a map to be absolute neighbourhood retract in a class of compact, to be

$Q$ -manifold or Hilbetr cube (finite sum of Hilbert cube).

Keywords: propability measure, compact Hausdorff space (compact), retract,

$A(N)R$ -space.

Received: 05.09.2018
Revised: 15.11.2018
Accepted: 19.12.2018

English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 10, Pages 24–32
DOI: https://doi.org/10.3103/S1066369X19100049

Bibliographic databases:

Document Type: Article

UDC: 515.12

Language: Russian

Citation: A. A. Zaitov, “Geometrical and topological properties of a subspace

$P_f(X)$ of probability measures”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 10, 28–37; Russian Math. (Iz. VUZ), 63:10 (2019), 24–32

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/ivm9504

https://www.mathnet.ru/eng/ivm/y2019/i10/p28

This publication is cited in the following 13 articles:

A. Ya. Ishmetov, “Functor of Idempotent Probability Measures with Compact Support and Open Mappings”, J Math Sci, 278:3 (2024), 463
Abror Tagaymurotov, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 3045, PROBLEMS IN THE TEXTILE AND LIGHT INDUSTRY IN THE CONTEXT OF INTEGRATION OF SCIENCE AND INDUSTRY AND WAYS TO SOLVE THEM: PTLICISIWS-2, 2024, 020012
R. E. Jiemuratov, “On the Dimension of the Space of Weakly Additive Functionals”, Math. Notes, 113:3 (2023), 345–355
A. A. Zaitov, D. T. Eshkobilova, “Dugundji Compacta and the Space of Idempotent Probability Measures”, Math. Notes, 114:4 (2023), 433–442
Kh. Kholturaev, “On $Z$ -Sets in the Space of Idempotent Probability Measures”, Math. Notes, 111:6 (2022), 940–953
Adilbek Atakhanovich Zaitov, Khamidjon Kurbanov, “When is the space of semi-additive functionals an absolute (neighbourhood) retract?”, PIGC, 15:2 (2022), 86
A. A. Zaitov, Kh. F. Kholturayev, “On Some Properties of Infinite Iterations of the Functor of Idempotent Probability Measures”, Lobachevskii J Math, 43:8 (2022), 2341
A. A. Borubaev, D. T. Eshkobilova, “The functor of idempotent probability measures and maps with uniformity properties of uniform spaces”, Eurasian Math. J., 12:3 (2021), 29–41
A. Ya. Ishmetov, “Funktor idempotentnykh veroyatnostnykh mer s kompaktnym nositelem i otkrytye otobrazheniya”, Nauka — tekhnologiya — obrazovanie — matematika — meditsina, SMFN, 67, no. 4, Rossiiskii universitet druzhby narodov, M., 2021, 693–706
Kh. F. Kholturayev, “Geometrical properties of the space of idempotent probability measures”, Appl. Gen. Topol., 22:2 (2021), 399–415
A. A. Zaitov, “On a metric on the space of idempotent probability measures”, Appl. Gen. Topol., 21:1 (2020), 35–51
Kh. Kurbanov, S. Yodgarov, “A functor IS in the Category Compact Hausdorff Spaces”, BSP, 6:3 (2020), 13
A. A. Zaitov, A. Ya. Ishmetov, “Homotopy Properties of the Space $I_f(X)$ of Idempotent Probability Measures”, Math. Notes, 106:4 (2019), 562–571

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Russian Mathematics (Izvestiya VUZ. Matematika)

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