NON-UNIFORMLY CONTINUOUS NEAREST POINT MAPS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F24%3A00379050" target="_blank" >RIV/68407700:21230/24:00379050 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1090/proc/16916" target="_blank" >https://doi.org/10.1090/proc/16916</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1090/proc/16916" target="_blank" >10.1090/proc/16916</a>

Result language
angličtina
Original language name
NON-UNIFORMLY CONTINUOUS NEAREST POINT MAPS
Original language description
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any non-singleton compact and convex subset is continuous but not uniformly continuous. The space we construct is locally uniformly convex, which ensures the continuity of all these nearest point maps. Moreover, we prove that every infinitedimensional separable Banach space is arbitrarily close (in the Banach-Mazur distance) to one satisfying the above conditions.
Czech name
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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
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA23-04776S" target="_blank" >GA23-04776S: Interplay of algebraic, metric, geometric and topological structures on Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
C - Předmět řešení projektu podléhá obchodnímu tajemství (§ 504 Občanského zákoníku), ale název projektu, cíle projektu a u ukončeného nebo zastaveného projektu zhodnocení výsledku řešení projektu (údaje P03, P04, P15, P19, P29, PN8) dodané do CEP, jsou upraveny tak, aby byly zveřejnitelné.

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