\begin{definition}[Definition:Basis (Topology)/Specification of Topology]
As a way of specifying a particular topology on a set, we can say:
:''Let $\tau$ be the topology which has the sets ... as a basis.''
In such a case, those sets should all satisfy the axioms for a synthetic basis $(\text B 1)$ and $(\text B 2)$.
\end{definition}