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 ).