\begin{definition}[Definition:Borel Sigma-Algebra/Borel Set]
Let $\struct {S, \tau}$ be a topological space.
Let $\map \BB {S, \tau}$ be the Borel $\sigma$-algebra of $\struct {S, \tau}$.
The elements of $\map \BB {S, \tau}$ are called the '''Borel (measurable) sets''' of $\struct {S, \tau}$.
\end{definition}