Axiom:Filter on Set Axioms/Axioms 1

Definition
Let $S$ be a set.

Let $\powerset S$ denote the power set of $S$.

Let $\FF \subset \powerset S$.

$\FF$ is a filter on $S$ $\FF$ satisfies the following axioms:

These criteria ae called the filter on set axioms.

Also see

 * Definition:Filter on Set


 * Equivalence of Definitions of Filter on Set