Baire property of spaces of [0, 1]-valued continuous functions
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
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Baire property of spaces of [0, 1]-valued continuous functions
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| Автор |
Osipov, A. V.
Pytkeev, E. G. |
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| Тематика |
ALMOST OPEN MAP
BAIRE PROPERTY FUNCTION SPACE PEANO CONTINUUM FUNCTIONAL ANALYSIS ALMOST OPEN MAP BAIRE PROPERTY CLOSED SUBSETS CONTINUOUS FUNCTIONS DENSE SUBSET FUNCTION SPACES OPEN MAPS PEANO CONTINUUM POINTWISE CONVERGENCE TOPOLOGICAL SPACES TOPOLOGY |
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| Описание |
A topological space X is Baire if the intersection of any sequence of open dense subsets of X is dense in X. Let Cp(X, [0 , 1]) denote the space of all continuous [0, 1]-valued functions on a Tychonoff space X with the topology of pointwise convergence. In this paper, we have obtained a characterization for the function space Cp(X, [0 , 1]) to be Baire for a Tychonoff space X all separable closed subsets of which are C∗-embedded. In particular, this characterization holds for normal spaces and, hence, for metrizable spaces. Moreover, we established that the space Cp(X, [0 , 1]) is Baire if and only if Cp(X, K) is Baire for a Peano continuum K. © 2022, The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid.
The authors would like to thank Evgenii Reznichenko for several valuable comments on Propositions 3.1 and 3.2 and the referee for careful reading and valuable suggestions. |
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| Дата |
2024-04-05T16:18:40Z
2024-04-05T16:18:40Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/submittedVersion |
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| Идентификатор |
Osipov, AV & Pytkeev, EG 2023, 'Baire property of spaces of [0, 1]-valued continuous functions', Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Том. 117, № 1, 38. https://doi.org/10.1007/s13398-022-01371-w
Osipov, A. V., & Pytkeev, E. G. (2023). Baire property of spaces of [0, 1]-valued continuous functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 117(1), [38]. https://doi.org/10.1007/s13398-022-01371-w 1578-7303 Final All Open Access, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85143602628&doi=10.1007%2fs13398-022-01371-w&partnerID=40&md5=dc9e3f741092009311db522af70756f9 https://arxiv.org/pdf/2203.05976 http://elar.urfu.ru/handle/10995/130337 10.1007/s13398-022-01371-w 85143602628 000895683000001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
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| Формат |
application/pdf
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| Издатель |
Springer-Verlag Italia s.r.l.
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| Источник |
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas |
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