$G_{\delta }$ 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 $[-1,+1]\in ℝ$ is a $G_{\delta }$ set because

$$[-1,+1]=\bigcap _{n=1}^{\mathrm{\infty }}(-\frac{1}{n}-1,\frac{1}{n}+1)$$

Title	$G_{\delta }$ set
Canonical name	GdeltaSet
Date of creation	2013-03-22 14:38:02
Last modified on	2013-03-22 14:38:02
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	7
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 54A05
Related topic	F_sigmaSet
Related topic	PavedSet
Related topic	PavedSpace