Definition:Comparable Filters 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 $S$.

$\FF$ and $\FF'$ are comparable if and only if one is finer (or coarser) than the other.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Filters