Length-metric space

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

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.

Relation with other properties

Stronger properties

Weaker properties