Definition:Borel Sigma-Algebra/Topological Space

Definition
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 $S$.