Note on the Banach Problem 1 of condensations of Banach spaces onto compacta
Электронный научный архив УРФУ
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Note on the Banach Problem 1 of condensations of Banach spaces onto compacta
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| Автор |
Osipov, A. V.
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| Тематика |
BANACH PROBLEM
CONDENSATION DENSITY METRIC COMPACT SPACE |
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| Описание |
It is consistent with any possible value of the continuum c that every infinite-dimensional Banach space of density ≤ c condenses onto the Hilbert cube. Let µ < c be a cardinal of uncountable cofinality. It is consistent that the continuum be arbitrary large, no Banach space X of density γ, µ < γ < c, condenses onto a compact metric space, but any Banach space of density µ admits a condensation onto a compact metric space. In particular, for µ = ω1, it is consistent that c is arbitrarily large, no Banach space of density γ, ω1 < γ < c, condenses onto a compact metric space. These results imply a complete answer to the Problem 1 in the Scottish Book for Banach spaces: When does a Banach space X admit a bijective continuous mapping onto a compact metric space?. © 2023, University of Nis. All rights reserved.
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| Дата |
2024-04-05T16:15:44Z
2024-04-05T16:15:44Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Osipov, AV 2023, 'Note on the Banach Problem 1 of condensations of Banach spaces onto compacta', Filomat, Том. 37, № 7, стр. 2183-2186. https://doi.org/10.2298/FIL2307183O
Osipov, A. V. (2023). Note on the Banach Problem 1 of condensations of Banach spaces onto compacta. Filomat, 37(7), 2183-2186. https://doi.org/10.2298/FIL2307183O 0354-5180 Final All Open Access, Bronze, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85148380594&doi=10.2298%2fFIL2307183O&partnerID=40&md5=b3eb3fc0b7ddceec9e8ac67482a46c6f http://www.doiserbia.nb.rs/ft.aspx?id=0354-51802307183O http://elar.urfu.ru/handle/10995/130206 10.2298/FIL2307183O 85148380594 000932458300016 |
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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 |
University of Nis
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| Источник |
Filomat
Filomat |
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