Let $(X,\mathscr{T})$ be a Topological Space. Let $\mathcal{B}(X)$ be the smallest σ-algebra containing $\mathscr{T}.$ Elements of $\mathcal{B}(X)$ are called Borel subsets and $$\mathcal{B}(X):=\sigma(\mathscr{T})$$ # Definition (437) Denote by $\mathcal{B}(X)$ the smallest σ-algebra on $X\subseteq\mathbb{R}^{n}$ (where $X$ is a metric space with metric $d$) containing the Open subsets of $X$ (i.e. the σ-algebra generated by the open sets) we call this the Borel σ-algebra. Subsets from $\mathcal{B}(X)$ are called Borel Sets.