# metric space

## metric space

*noun*

## Definition of *METRIC SPACE*

**:**a mathematical set for which a metric is defined for any pair of elements

## First Known Use of *METRIC SPACE*

## metric space

*noun*

*(Concise Encyclopedia)*

In mathematics, a set of objects equipped with a concept of distance. The objects can be thought of as points in space, with the distance between points given by a distance formula, such that: (1) the distance from point A to point B is zero if and only if A and B are identical, (2) the distance from A to B is the same as from B to A, and (3) the distance from A to B plus that from B to C is greater than or equal to the distance from A to C (the triangle inequality). Two- and three-dimensional Euclidean spaces are metric spaces, as are inner product spaces, vector spaces, and certain topological spaces (*see* topology).

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