54-00-RegularlyOpen.tex

\documentclass[12pt]{article}
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\pmcanonicalname{RegularlyOpen}
\pmcreated{2013-03-22 12:19:43}
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\pmtitle{regularly open}
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\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{54-00}

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\begin{document}
Given a topological space $(X,\tau)$, a \emph{regularly open set} is an open set $A\in \tau$ such that 
$$\mathrm{int}\, \overline{A}=A$$
(the interior of the closure is the set itself).

An example of non regularly open set on the standard topology for $\R$ is
$A=(0,1)\cup(1,2)$ since $\mathrm{int}\overline{A}=(0,2)$.
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