Metric Space

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number g(x,y). A metric space must also satisfy

1. g(x,y)=0 iff x=y,

2. g(x,y)=g(y,x),

3. The triangle inequality g(x,y)+g(y,z)>=g(x,z).

See also

Complete Metric Space, Metric, Metric Tensor, Space, Triangle Inequality, Universal Space Explore this topic in the MathWorld classroom

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References

Munkres, J. R. Topology: A First Course, 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 2000.Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, 1976.

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Metric Space

Cite this as:

Weisstein, Eric W. "Metric Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MetricSpace.html

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