\begin{definition}[Definition:Generator Set of Filter]
Let $L = \left({S, \wedge, \preceq}\right)$ be a meet semilattice.
Let $F$ be a filter on $L$.
The '''generator set''' $G$ of $F$ is defined as follows:
:$F = \left({\operatorname{fininfs}\left({G}\right)}\right)^\succeq$
where
:$\operatorname{fininfs}\left({G}\right)$ denotes the finite infima set of $G$,
:$G^\succeq$ denotes the upper closure of $G$.
\end{definition}