\begin{definition}[Definition:Convergent Filter]
Let $\struct {S, \tau}$ be a topological space.
Let $\FF$ be a filter on $S$.
Then $\FF$ '''converges''' to a point $x \in S$ {{iff}}:
:$\forall N_x \subseteq S: N_x \in \FF$
where $N_x$ is a neighborhood of $x$.
That is, a filter '''converges''' to a point $x$ {{iff}} every neighborhood of $x$ is an element of that filter.
If there is a point $x \in S$ such that $\FF$ '''converges''' to $x$, then $\FF$ is '''convergent'''.
\end{definition}