\begin{definition}[Definition:Borel Sigma-Algebra/Topological Space]
Let $\struct {S, \tau}$ be a topological space
The '''Borel sigma-algebra''' $\map \BB {S, \tau}$ of $\struct {S, \tau}$ is the $\sigma$-algebra generated by $\tau$.
That is, it is the $\sigma$-algebra generated by the set of open sets in $S$.
\end{definition}