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Tom LaGatta
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Tom LaGatta
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Better terminology than "equivalence class of functions"

Let $X = C(\mathbb R)$ be the Fréchet space of real-valued continuous functions. For each $f \in X$ and each compact set $D \subseteq \mathbb R$, let $$[f]_D = \{ g \in X : \mbox{$g(t) = f(t)$ for all $t \in D$} \} $$ be the equivalence class of functions which agree with $f$ on the set $D$.

I refer to this object frequently in a paper I am writing. The notation $[f]_D$ is short and sweet, but the terminology "equivalence class of functions" is too clunky.

Question: Is there a better name for the object $[f]_D$?