Any space whose elements are points, and between any two of which a non-negative real number can be defined as the distance between the points; an example is Euclidean space
a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
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)