\begin{definition}[Definition:Convergent Filter Basis]
Let $\struct {S, \tau}$ be a topological space.
Let $\BB$ be a filter basis of a filter $\FF$ on $S$.
Then $\BB$ '''converges''' to a point $x \in S$ {{iff}}:
:$\forall N_x \subseteq S: \exists B \in \BB: B \subseteq N_x$
where $N_x$ is a neighborhood of $x$.
That is, a filter basis is '''convergent''' to a point $x$ if every neighborhood of $x$ contains some set of that filter basis.
\end{definition}