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" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters.
Hausdorff spaces are named for 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.
Read more about Hausdorff Space: Definitions, Equivalences, Examples and Counterexamples, Properties, Preregularity Versus Regularity, Variants, Algebra of Functions, Academic Humour
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“The within, all that inner space one never sees, the brain and the heart and other caverns where thought and feeling dance their sabbath.”
—Samuel Beckett (1906–1989)