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Revision as of 06:38, 23 May 2002 by Magnus Manske (talk | contribs) (-talk)(diff) ← Previous revision | Latest revision (diff) | Newer revision → (diff)A Hausdorff space is a topological space in which any two distinct points have disjoint neighbourhoods. Hausdorff spaces are also called T2 spaces. They are named after Felix Hausdorff.
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 Tychonoff space.
Note: there is a (fairly poor) mathematicians' joke that serves as a reminder of the meaning of this term: in a Hausdorff space, points are "housed off". This pun is so lousy one is almost certain to remember it.