@misc{10481/96618,
year = {2024},
month = {10},
url = {https://hdl.handle.net/10481/96618},
abstract = {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.},
organization = {Grants PID2021-122126NB-C31 (the first author) and PID2021-
122126NB-C33 (the second author), funded by MICIU/AEI/10.13039/501100011033 and by
ERDF/EU},
organization = {FPU19/04085 MIU (Spain)},
organization = {Junta de Andalucia Grant FQM-0185 by GA23-04776S project (Czech Republic) and
by SGS22/053/OHK3/1T/13 project (Czech Republic)},
organization = {French ANR project No. ANR-20-CE40-0006},
publisher = {American Mathematical Society},
title = {Non-uniformly continuous nearest point maps},
doi = {10.1090/proc/16916},
author = {Medina Sabino, Rubén and Quilis, Andrés},
}