G-delta Set

Definition

Consider a Topological Space $(X,\mathcal{T})$ and a subset $A\subset X$. The subset $A$ is a $G_{\delta }$ set if there exists a countable collection of open sets $\{U_i{\}}_{i\in \mathbb{N}}$ whose intersection is $A$. $\exists \{U_i{\}}_{i\in \mathbb{N}}\text{s.t.}{U}_i\in \mathcal{T}\text{and}{\bigcap }_{i\in \mathbb{N}}{U}_i=A$