Tangent spaces to metric spaces and to their subspaces

TL;DR

This paper explores tangent spaces in general metric spaces and their subspaces, establishing conditions for when different subspaces have isometric tangent spaces at a common point.

Contribution

It provides a complete characterization of when subspaces of a metric space have isometric tangent spaces at a shared point.

Findings

Conditions for isometric tangent spaces between subspaces are fully determined

Introduces metric space valued derivatives and tangent space concepts

Advances understanding of local geometric structure in metric spaces

Abstract

We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces are completely determinated.