Definition:Borel Sigma-Algebra/Borel Set

Definition
Let $\struct {S, \tau}$ be a topological space.

Let $\map {\mathcal B} {S, \tau}$ be the Borel $\sigma$-algebra of $\struct {S, \tau}$.

The elements of $\map {\mathcal B} {S, \tau}$ are called the Borel (measurable) sets of $\struct {S, \tau}$.