Definition:Filter/Proper Filter
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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 $S$
- $\FF \ne S$
That is, if and only if $\FF$ is a proper subset of $S$.
Also see
- Results about filter theory can be found here.