Definition

Let $(X,\mathscr{T})$ be a topological space. Let $\mathcal{B}$ be the Borel σ-algebra associated with $\mathscr{T}$. Then we say $$G_{\delta}\text{ sets}:=\bigcap_{n\in\mathbb{N}}A_{n}\quad\forall(A_{n})_{n\in\mathbb{N}}\subset \mathscr{T}$$or $$\text{Countable intersections of open sets}:=G_{\delta}\text{ sets}$$ ## Example $$\mathbb{R}\setminus \mathbb{Q}\in\mathcal{B}(G_{\delta})$$