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Every metric space of weight admits a condensation onto a Banach space. / Osipov, A. V.; Pytkeev, E. G.
In: Topology and its Applications, No. 330, 108486, 05.2023.

Research output: Contribution to journal › Article › peer-review

Harvard

Osipov, AV & Pytkeev, EG 2023, 'Every metric space of weight admits a condensation onto a Banach space', Topology and its Applications, no. 330, 108486. https://doi.org/10.1016/j.topol.2023.108486

APA

Osipov, A. V., & Pytkeev, E. G. (2023). Every metric space of weight admits a condensation onto a Banach space. Topology and its Applications, (330), [108486]. https://doi.org/10.1016/j.topol.2023.108486

Vancouver

Osipov AV, Pytkeev EG. Every metric space of weight admits a condensation onto a Banach space. Topology and its Applications. 2023 May;(330):108486. doi: 10.1016/j.topol.2023.108486

Author

Osipov, A. V. ; Pytkeev, E. G. / Every metric space of weight admits a condensation onto a Banach space. In: Topology and its Applications. 2023 ; No. 330.

BibTeX

@article{4278847448674ddea3014d557036e5d4,
title = "Every metric space of weight admits a condensation onto a Banach space",
abstract = "In this paper, we have proved that for each cardinal number λ such that λ=λℵ0 a metric space of weight λ admits a bijective continuous mapping onto a Banach space of weight λ. Then, we get that every metric space of weight continuum admits a bijective continuous mapping onto the Hilbert cube. This resolves the famous Banach's Problem (when does a metric (possibly Banach) space X admit a bijective continuous mapping onto a compact metric space?) in the class of metric spaces of weight continuum. Also we get that every metric space of weight λ=λℵ0 admits a bijective continuous mapping onto a Hausdorff compact space. This resolves the Alexandroff Problem (when does a Hausdorff space X admit a bijective continuous mapping onto a Hausdorff compact space?) in the class of metric spaces of weight λ=λℵ0. {\textcopyright} 2023 Elsevier B.V.",
author = "Osipov, {A. V.} and Pytkeev, {E. G.}",
note = "The authors would like to thank the referee for careful reading and valuable comments.",
year = "2023",
month = may,
doi = "10.1016/j.topol.2023.108486",
language = "English",
journal = "Topology and its Applications",
issn = "0166-8641",
publisher = "Elsevier",
number = "330",

}

RIS

TY - JOUR

T1 - Every metric space of weight admits a condensation onto a Banach space

AU - Osipov, A. V.

AU - Pytkeev, E. G.

N1 - The authors would like to thank the referee for careful reading and valuable comments.

PY - 2023/5

Y1 - 2023/5

N2 - In this paper, we have proved that for each cardinal number λ such that λ=λℵ0 a metric space of weight λ admits a bijective continuous mapping onto a Banach space of weight λ. Then, we get that every metric space of weight continuum admits a bijective continuous mapping onto the Hilbert cube. This resolves the famous Banach's Problem (when does a metric (possibly Banach) space X admit a bijective continuous mapping onto a compact metric space?) in the class of metric spaces of weight continuum. Also we get that every metric space of weight λ=λℵ0 admits a bijective continuous mapping onto a Hausdorff compact space. This resolves the Alexandroff Problem (when does a Hausdorff space X admit a bijective continuous mapping onto a Hausdorff compact space?) in the class of metric spaces of weight λ=λℵ0. © 2023 Elsevier B.V.

AB - In this paper, we have proved that for each cardinal number λ such that λ=λℵ0 a metric space of weight λ admits a bijective continuous mapping onto a Banach space of weight λ. Then, we get that every metric space of weight continuum admits a bijective continuous mapping onto the Hilbert cube. This resolves the famous Banach's Problem (when does a metric (possibly Banach) space X admit a bijective continuous mapping onto a compact metric space?) in the class of metric spaces of weight continuum. Also we get that every metric space of weight λ=λℵ0 admits a bijective continuous mapping onto a Hausdorff compact space. This resolves the Alexandroff Problem (when does a Hausdorff space X admit a bijective continuous mapping onto a Hausdorff compact space?) in the class of metric spaces of weight λ=λℵ0. © 2023 Elsevier B.V.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85150340682

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=000959753200001

U2 - 10.1016/j.topol.2023.108486

DO - 10.1016/j.topol.2023.108486

M3 - Article

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 330

M1 - 108486

ER -

ID: 36195375