Definition

Let $(X,\mathscr{T})$ be a topological space. Let $\mathcal{B}$ be the Borel σ-algebra associated with $\mathscr{T}$. Then we say $$F_{\sigma}:=\bigcup_{n\in\mathbb{N}}C_{n}\quad\forall(C_{n})_{n\in\mathbb{N}}\text{ s.t. }C_{n}^{c}\in\mathscr{T},\ \forall n\in\mathbb{N}$$ or $$\text{Countable unions of }\textbf{CLOSED} \text{ sets}:=F_{\sigma}\text{ sets}$$ ## Example $$\mathbb{Q}\in\mathcal{B}(F_{\sigma})$$