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A Nonnegative function $g(x,y)$ describing the ``Distance'' between neighboring points for a given Set. A metric satisfies the Triangle Inequality

g(x,y)+g(y,z)\geq g(x,z)

and is symmetric, so


A Set possessing a metric is called a Metric Space. When viewed as a Tensor, the metric is called a Metric Tensor.

See also Cayley-Klein-Hilbert Metric, Distance, Fundamental Forms, Hyperbolic Metric, Metric Entropy, Metric Equivalence Problem, Metric Space, Metric Tensor, Part Metric, Riemannian Metric, Ultrametric


Gray, A. ``Metrics on Surfaces.'' Ch. 13 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 251-265, 1993.

© 1996-9 Eric W. Weisstein