= Regular topological space
= Regularity of a topological space
{synonym}
A <topological space> is regular when a <point> and a <closed set> not containing it have disjoint <open neighborhoods>. Equivalently, for every <point> $x$ in an <open set> $U$, there is an open $W$ with $x\in W\subseteq\overline W\subseteq U$. To obtain shrinking, separate $x$ from the closed complement of $U$; the <closure> of the <point>'s <neighborhood> avoids the other <neighborhood>. Conversely use such a shrinking and the complement of its <closure>. This definition alone does not require $T_1$.
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