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| A '''Hausdorff space''' is a ] in which distinct points have disjoint neighbourhoods. Hausdorff spaces are also called T<sub>2</sub> spaces. | A '''Hausdorff space''' is a ] in which distinct points have disjoint neighbourhoods. Hausdorff spaces are also called T<sub>2</sub> spaces. They are named after ]. | ||
| Limits of ] (when they exist) are unique in Hausdorff spaces. | Limits of ] (when they exist) are unique in Hausdorff spaces. | ||
| A ] ''X'' is Hausdorff iff the diagonal {(''x'',''x'') : ''x'' in ''X''} is a closed subspace of the Cartesian product of ''X'' with itself. | A ] ''X'' is Hausdorff ] the diagonal {(''x'',''x'') : ''x'' in ''X''} is a closed subspace of the Cartesian product of ''X'' with itself. | ||
| See also ], ] and ]. | See also ], ] and ]. | ||
Revision as of 13:14, 20 August 2001
A Hausdorff space is a topological space in which 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 Tychonov space.