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 $S$

if and only if:

$\FF \ne S$

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


Also see

  • Results about filter theory can be found here.