# $G_{\delta}$ set

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 $F_{\sigma}$ set (http://planetmath.org/F_sigmaSet).

For example, the closed interval $[-1,+1]\in\mathbb{R}$ is a $G_{\delta}$ set because

 $[-1,+1]=\bigcap_{n=1}^{\infty}\left(-{1\over n}-1,{1\over n}+1\right)$
Title $G_{\delta}$ set GdeltaSet 2013-03-22 14:38:02 2013-03-22 14:38:02 rspuzio (6075) rspuzio (6075) 7 rspuzio (6075) Definition msc 54A05 F_sigmaSet PavedSet PavedSpace