Definition:Coarser Filter on Set

Definition
Let $S$ be a set.

Let $\mathcal P \left({S}\right)$ be the power set of $S$.

Let $\mathcal F, \mathcal F' \subset \mathcal P \left({S}\right)$ be two filters on $S$.

Let $\mathcal F \subseteq \mathcal F'$.

Then $\mathcal F$ is coarser than $\mathcal F$.

Also known as
If $\mathcal F$ is a coarser filter than $\mathcal F'$, then $\mathcal F'$ can also be referred to as a superfilter of $\mathcal F$.

Also see

 * Definition:Finer Filter on Set
 * Definition:Strictly Finer Filter on Set


 * Definition:Comparable Filters on Set