Length-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.

Stronger properties

 * Weaker than::Geodesic metric space

Weaker properties

 * Stronger than::Path-connected metric space