See also
Bi-Lipschitz Map,
Complete Metric Space,
Geodesic Metric Space,
Gromov-Hausdorff Distance,
Length
Space,
Lipschitz Function,
Metric,
Metric k-Median,
Metric
Space Magnitude,
Metric Tensor,
Space,
Triangle Inequality,
Universal
Space,
Wasserstein Distance Explore this topic in the MathWorld classroom
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References
Munkres, J. R. Topology, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2000.Rudin, W.
Principles
of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, 1976.Referenced
on Wolfram|Alpha
Metric Space
Cite this as:
Weisstein, Eric W. "Metric Space." From
MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MetricSpace.html
Subject classifications
with a global distance function
(the metric 
) that, for every two points 
in 
, gives the distance between them
as a nonnegative real
number 
.
A metric space must also satisfy the following conditions for
all 
(Rudin 1976, p. 30; Munkres 2000, p. 119):
iff 
,
,
.
