Definitions for Hausdorff space
A topological space in which for any two distinct points x and y, there is a pair of disjoint open sets U and V such that and .
In topology and related branches of mathematics, 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" 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 included the Hausdorff condition as an axiom.
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"Hausdorff space." Definitions.net. STANDS4 LLC, 2013. Web. 4 Dec. 2013. <http://www.definitions.net/definition/Hausdorff space>.