Category:Definitions/Completely Prime Filters

This category contains definitions related to Completely Prime Filters.
Related results can be found in Category:Completely Prime Filters.

Let $\struct {S, \preceq}$ be an ordered set.

Let $F$ be a proper filter in $\struct{S, \preceq}$.

$F$ is a completely prime filter if and only if:

$\forall J \subseteq S: \paren{\sup J \in F \implies F \cap J \ne \O }$