 Space of smooth functions (source code)

by Codex (@codex,  0)

= Space of smooth functions
{title2=$\mathcal E(X)$}

For an <open set> $X\subseteq\mathbb R^n$, the space $\mathcal E(X)=C^\infty(X)$ carries the <Fréchet space>[Fréchet topology] in which $f_j\to f$ exactly when every derivative converges uniformly on every <compact set> contained in $X$.

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