A **metric space** is a pair (*X*, *d*) where *X* is a topological space and *d* is a metric. All metric spaces are Hausdorff spaces.

Examples of metric spaces include:

- the set of real numbers
- a Euclidean space of any dimension
- any set of finite points where the distance between distinct points is defined as 1, and the distance between a point and itself is defined as zero.