2023/11/22 by Quilis, Andrés, Zoca, Abraham Rueda
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2311.13289
We introduce the notion of (almost isometric) local retracts in metric space as a natural non-linear version of the concepts of locally complemented and almost isometric ideals from Banach spaces. We prove that given two metric spaces N⊆ M there always exists an almost isometric local retract S⊆ M with N⊆ S and 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. Different examples and counterexamples are exhibited.