Hausdorff space

<p>In <a href="/facts/Topology/2EqW47cU">topology</a> and related branches of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a Hausdorff space , T2 space or separated space, is a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> where distinct points have <a href="/facts/Disjoint_sets/nLr8XRVd">disjoint</a> <a href="/facts/Neighbourhood_(mathematics)/XHKgrpkp">neighbourhoods</a>.  Of the many <a href="/facts/Separation_axiom/s4CKf8gp">separation axioms</a> that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of <a href="/facts/Limit_of_a_sequence/Ktge2RwL">limits</a> of <a href="/facts/Limit_of_a_sequence/Ktge2RwL">sequences</a>, <a href="/facts/Net_(topology)/msmsvMTT">nets</a>, and <a href="/facts/Filter_(topology)/5vQbHcpE">filters</a>.
</p><p>Hausdorff spaces are named after <a href="/facts/Felix_Hausdorff/Rn6DuY2x">Felix Hausdorff</a>, one of the founders of topology. Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an <a href="/facts/Axiom/mLjP14Mc">axiom</a>.
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Hausdorff space open-in-new

Hausdorff space