In the above definitions, it suffices to check that \mathcal{B} is finer than some (or equivalently, finer than every) neighborhood base in (X, \tau) of the point or set (for example, such as \tau(x) = \{U \in \tau : x \in U\} or \tau(S) = {\textstyle\bigcap\limits_{s \in S}} \tau(s) when S \neq \varnothing).
