$G_\delta$ setG_deltaSet2004-09-24 02:51:032004-09-25 01:06:38Definition% this is the default PlanetMath preamble. as your knowledge
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% define commands hereA $G_\delta$ 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
$$[-1,+1] = \bigcap_{n=1}^\infty \left( -{1 \over n}-1,{1 \over n}+1 \right)$$