A complete metric space without non-trivial separable Lipschitz retracts

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00367881" target="_blank" >RIV/68407700:21230/23:00367881 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2023.109941" target="_blank" >https://doi.org/10.1016/j.jfa.2023.109941</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2023.109941" target="_blank" >10.1016/j.jfa.2023.109941</a>

Result language
angličtina
Original language name
A complete metric space without non-trivial separable Lipschitz retracts
Original language description
We construct a complete metric space M of cardinality continuum such that every non-singleton closed separable subset of M fails to be a Lipschitz retract of M. This provides a metric analogue to the various classical and recent examples of Banach spaces failing to have linearly complemented subspaces of prescribed smaller density character. (c) 2023 Elsevier Inc. All rights reserved.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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