A basis for a topology $\tau$ on a set $X$ is a collection $\mathcal B$ of subsets of $X$ such that
- All points are contained in at least one element of $\mathcal B$, and
- If $x\in B’\cap B’’$ then there exists at least one $B\in \mathcal B$ such that $x\in B \subset B’\cap B’’$.