Metric

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

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

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

References

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