# metric space

A metric space is a set of objects together with a concept of distance defined on its elements; specifically, a function from pairs of elements of the set to the non-negative real numbers satisfying certain conditions. (See metric.)

The commonest metric spaces are the number sets themselves, with distance defined by difference, and the Cartesian plane with distance defined by the well-known distance formula. Other important metric spaces include the vector spaces and Hilbert space.