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


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