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Regular space
open-in-new
<p>In <a href="/facts/Topology/2EqW47cU">topology</a> and related fields of <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a <a href="/facts/Topological_space/v2ut7CbK">topological space</a> <i>X</i> is called a regular space if every <a href="/facts/Closed_subset/upYnRTUj">closed subset</a> <i>C</i> of <i>X</i> and a point <i>p</i> not contained in <i>C</i> have non-overlapping <a href="/facts/Open_neighborhood/XHKgrpkp">open neighborhoods</a>. Thus <i>p</i> and <i>C</i> can be <a href="/facts/Separated_sets/NxVgxIF9">separated</a> by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "a regular <a href="/facts/Hausdorff_space/gbKIrusl">Hausdorff space</a>". These conditions are examples of <a href="/facts/Separation_axiom/s4CKf8gp">separation axioms</a>. </p>