\begin{definition}[Definition:Finer Filter on Set]
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 $\FF$.
\end{definition}