Definition:Filter/Proper Filter

Definition
Let $\struct {S, \preccurlyeq}$ be an ordered set. Let $\FF$ be a filter on $\struct {S, \preccurlyeq}$.

Then:
 * $\FF$ is a proper filter on $S$


 * $\FF \ne S$
 * $\FF \ne S$

That is, $\FF$ is a proper subset of $S$.

Also see

 * Definition:Filter on Set