Hausdorff space

A Hausdorff space is a topological space in which distinct points have disjoint neighbourhoods. Hausdorff spaces are also called T₂ spaces.

Limits of sequences (when they exist) are unique in Hausdorff spaces.

A topological space X is Hausdorff iff the diagonal {(x,x) : x in X} is a closed subspace of the Cartesian product of X with itself.

See also topology, compact space and Tychonov space.