# Definition:Generator Set of Filter

## Definition

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 $G$.