Definition:Coarser Filter on Set

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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 coarser than $\FF$.


Strictly Coarser

Let $\FF \subset \FF'$, that is, $\FF \subseteq \FF'$ but $\FF \ne \FF'$.

Then $\FF'$ is strictly coarser than $\FF$.


Also known as

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


Also see


Sources