(Almost isometric) local retracts in metric spaces
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 ⊆ M there always exists an almost isometric local retract S ⊆ M with N ⊆ S and d e n s ( N ) = d e n s ( 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.
Authors
- Andrés Quilis (ORCID: https://orcid.org/0000-0001-6022-9286)
- Abraham Rueda Zoca (ORCID: https://orcid.org/0000-0003-0718-1353)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Universidad de Granada (ES)
- Laboratoire de Mathématiques de Besançon (FR)
- Université de Franche-Comté (FR)
Publication Details
- Journal
- Journal of Functional Analysis
- Published
- 2024-08-13
- DOI
- https://doi.org/10.1016/j.jfa.2024.110627
- Citations
- 2
- Primary Topic
- Advanced Banach Space Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.89
Funders
- Fundación Séneca
- Ministerio de Ciencia, Innovación y Universidades
- Agence Nationale de la Recherche
- Ministerstvo Školství, Mládeže a Tělovýchovy
- Grantová Agentura České Republiky
- Generalitat Valenciana
- Junta de Andalucía
- Agencia Estatal de Investigación