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arXiv · 2311.13289

(Almost isometric) local retracts in metric spaces

Andrés Quilis·Abraham Rueda Zoca
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Abstract

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 $N\subseteq M$ there always exists an almost isometric local retract $S\subseteq M$ with $N\subseteq S$ 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.

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Andrés Quilis, Abraham Rueda Zoca. 2023-11-22. (Almost isometric) local retracts in metric spaces. https://arxiv.org/abs/2311.13289

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