All-set-homogeneous spaces

TL;DR

This paper classifies a specific subclass of length spaces that are all-set-homogeneous, meaning any partial isometry can be extended to a full isometry, contributing to the understanding of symmetric metric spaces.

Contribution

It provides a classification of a particular subclass of all-set-homogeneous length spaces, advancing the theory of symmetric metric spaces.

Findings

Classification of a subclass of all-set-homogeneous length spaces

Extension of partial isometries to full isometries in these spaces

Enhanced understanding of symmetry properties in metric spaces

Abstract

A metric space is said to be all-set-homogeneous if any of its partial isometries can be extended to a genuine isometry. We give a classification of a certain subclass of all-set-homogeneous length spaces.