Past exam of the options I course of the University of Oxford / 2012 / E / E2 / a / Solution

A basis of a topology $\mathcal{B}$ is a family of open subsets such that every open set is a union of members of $\mathcal{B}$. Equivalently, for every $U\in \mathcal{T}$ and $x\in U$, some $B\in \mathcal{B}$ satisfiesThe empty open set is represented by the empty union.