54A05-GdeltaSet.tex

\documentclass[12pt]{article}
\usepackage{pmmeta}
\pmcanonicalname{GdeltaSet}
\pmcreated{2013-03-22 14:38:02}
\pmmodified{2013-03-22 14:38:02}
\pmowner{rspuzio}{6075}
\pmmodifier{rspuzio}{6075}
\pmtitle{$G_\delta$ set}
\pmrecord{7}{36216}
\pmprivacy{1}
\pmauthor{rspuzio}{6075}
\pmtype{Definition}
\pmcomment{trigger rebuild}
\pmclassification{msc}{54A05}
\pmrelated{F_sigmaSet}
\pmrelated{PavedSet}
\pmrelated{PavedSpace}

\endmetadata

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\begin{document}
A $G_\delta$ set is a set which can be expressed as the intersection of a countable collection of open sets.  

The complement of a $G_\delta$ set is an \PMlinkname{$F_\sigma$ set}{F_sigmaSet}.

For example, the closed interval $[-1,+1] \in \mathbb{R}$ is a $G_\delta$ set because
 $$[-1,+1] = \bigcap_{n=1}^\infty \left( -{1 \over n}-1,{1 \over n}+1 \right)$$
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\end{document}