Recall: Basis

So, for some topology $\mathscr{T}$ a basis is some subset that generates $\mathscr{T}$ in the sense that for any $\mathcal{O}\in \mathscr{T}$ we can find a collection of open sets in our basis: $\{ B_{a} \}_{a\in A}\subset \mathscr{B}$ s.t. they equal the open set $\mathcal{O}$. This pretty much generalizes the notion of a Finite Basis from linear algebra.