A subcollection $\mathcal{B}\subseteq \mathscr{T}$ of a topology $\mathscr{T}$ on a topological space $X$ is a basis for the topology $\mathscr{T}$ if given an open set $U$ and point $p \in U$, there is an open set $B\in \mathcal{B}$ such that $p ∈ B ⊂ U$, i.e. $$\forall U\in \mathscr{T},\forall p \in U,\exists B\in \mathcal{B}:p \in B\subset U.$$We also say that $\mathcal{B}$ generates the topology $\mathscr{T}$ or that $\mathcal{B}$ is a basis for the topological space $X$.