# Length-metric space

From Topospaces

*This article defines a property that can be evaluated for a metric space*

## Contents

## Definition

A metric space is termed a **length-metric space** if the distance between any two points in it equals the infimum of the lengths of all the paths joining them. Here, the length of a path is defined as the supremum, over all partitions of the unit interval, of the sums of distances between the images of endpoints of each part.