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