Hausdorff space
Published:
A Hausdorff space, separated space or T2 space, is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the “Hausdorff condition” (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters.
Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology. Hausdorff’s original definition of a topological space (in 1914) included the Hausdorff condition as an axiom.
See also
Books
- Hazewinkel, Michiel, ed. (2001), Hausdorff space, Encyclopedia of Mathematics, Springer.