# metric space

## metric space

noun Mathematics.
a space with a metric defined on it.

Origin:
1925–30

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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Computing Dictionary

### metric space definition

mathematics
A set of points together with a function, d, called a metric function or distance function. The function assigns a positive real number to each pair of points, called the distance between them, such that:
1. For any point x, d(x,x)=0;
2. For any two distinct points x and y, d(x,y)>0;
3. For any two points x and y, not necessarily distinct,
d(x,y) = d(y,x).
4. For any three points x, y, and z, that are not necessarily distinct,
d(x,z) <= d(x,y) + d(y,z).
The distance from x to z does not exceed the sum of the distances from x to y and from y to z. The sum of the lengths of two sides of a triangle is equal to or exceeds the length of the third side.
(2003-06-26)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
It is not a metric space, for two distinct events, a photon leaving the sun eight minutes ago and its.
It is reified, locally, in those regions of a manifold where there are valid metric space type representations.
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