Definition:Filter/Proper Filter

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Definition

Let $\left({S, \preccurlyeq}\right)$ be an ordered set.

Let $\mathcal F$ be a filter on $\left({S, \preccurlyeq}\right)$.


Then $\mathcal F$ is a proper filter on $S$ if and only if $\mathcal F \ne S$.

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


Also see

  • Results about filters can be found here.