Definition:Finite Character/Mappings

Definition
Let $S$ and $T$ be sets.

Let $\FF$ be a set of mappings from subsets of $S$ to $T$.

That is, let $\FF$ be a set of partial mappings from $S$ to $T$.

Then $\FF$ has finite character for each partial mapping $f \subseteq S \times T$:


 * $f \in \FF$ for each finite subset $K$ of the domain of $f$, the restriction of $f$ to $K$ is in $\FF$.

Also see

 * Finite Character for Sets of Mappings
 * Cowen-Engeler Lemma, an equivalent of the Boolean Prime Ideal Theorem.