(Almost isometric) local retracts in metric spaces Quilis, Andrés Rueda Zoca, Abraham Absolute local retracts Almost isometric local retracts Finitely injective 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. 2024-09-12T07:19:00Z 2024-09-12T07:19:00Z 2024-08-21 journal article A. Quilis, A.RuedaZoca. 287 (2024) 110627. [https://doi.org/10.1016/j.jfa.2024.110627] https://hdl.handle.net/10481/94370 10.1016/j.jfa.2024.110627 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Elsevier