Let $T = (X, \mathcal{T})$ be a D1106: Topological space.
The Borel sigma-algebra on $X$ with respect to $T$ is the D11: Set $$\begin{equation} \sigma \langle \mathcal{T} \rangle : = \bigcap \{ \mathcal{F} :\mathcal{T} \subseteq \mathcal{F} \text{ and } \mathcal{F} \text{ is a sigma-algebra on } X \} \end{equation}$$