Definition:Finer Filter on Set

Definition
Let $S$ be a set.

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

Let $\FF, \FF' \subset \powerset S$ be two filters on $S$.

Let $\FF \subseteq \FF'$.

Then $\FF'$ is finer than $\FF$.

Also known as
A finer filter than $\FF$ can also be referred to as a superfilter of $\FF$.

Also see

 * Definition:Coarser Filter on Set
 * Definition:Strictly Coarser Filter on Set


 * Definition:Comparable Filters on Set