Definition:Finite Character/Mappings
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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 if and only if for each partial mapping $f \subseteq S \times T$:
- $f \in \FF$ if and only if 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.
Sources
- 1996: Eric Schechter: Handbook of Analysis and its Foundations: $\S 6.35$