Definition:Borel Sigma-Algebra/Borel Set

Definition
Let $\left({S, \tau}\right)$ be a topological space.

Let $\mathcal B \left({S, \tau}\right)$ be the Borel $\sigma$-algebra of $\left({S, \tau}\right)$.

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