Length-metric space: Difference between revisions
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===Stronger properties=== | ===Stronger properties=== | ||
* [[Geodesic metric space]] | * [[Weaker than::Geodesic metric space]] | ||
===Weaker properties=== | |||
* [[Stronger than::Path-connected metric space]] | |||
Latest revision as of 01:14, 25 November 2008
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.