@misc{10481/94370,
year = {2024},
month = {8},
url = {https://hdl.handle.net/10481/94370},
abstract = {We introduce the notion of (almost isometric) local retracts in metric space as a natural non-linear version of the concepts of ideals and almost isometric ideals in Banach spaces. We prove that given two metric spaces N⊆Mthere always exists an almost isometric local retract S⊆Mwith N⊆Sand dens(N) =dens(S). We also prove that metric spaces which are local retracts (respectively almost isometric local retracts) can be characterised in terms of a condition of extendability of Lipschitz functions (respectively almost isometries) between finite metric spaces. Various examples and counterexamples are exhibited.},
organization = {MCIN/AEI/10.13039/501100011033: grant PID2021-122126NB-C31 (Rueda Zoca), grant PID2021-122126NB-C33 (Quilis)},
organization = {GACR Grant GA23-04776S, Czech Ministry of Youth and Sport project SGS23/056/OHK3/1T/13 and by the French ANR project No. ANR-20-CE40-0006},
organization = {Junta de Andalucía: Grants FQM-0185 and PY20_00255},
organization = {Fundación Séneca: ACyT Región de Murcia grant 21955/PI/22},
organization = {Generalitat Valenciana project CIGE/2022/97},
publisher = {Elsevier},
keywords = {Absolute local retracts},
keywords = {Almost isometric local retracts},
keywords = {Finitely injective},
title = {(Almost isometric) local retracts in metric spaces},
doi = {10.1016/j.jfa.2024.110627},
author = {Quilis, Andrés and Rueda Zoca, Abraham},
}