A length space is a metric space whose metric is a length metric, so each distance
is the infimum of the lengths of paths
joining the two points (Lang 2013, p. 2).
Every geodesic metric space is a length space: a distance-minimizing path attains the infimum
in the defining condition (Lang 2013, p. 3).
See also
CAT(0) Space,
Geodesic Metric Space,
Length Metric,
Metric
Space
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References
Lang, U. Length Spaces. Lecture notes, version of
4 Nov 2013, pp. 2-3. https://people.math.ethz.ch/~lang/LengthSpaces.pdf.
Cite this as:
Weisstein, Eric W. "Length Space." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LengthSpace.html
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