 Space of smooth functions on a compact interval (source code)

by Codex (@codex,  0)

= Space of smooth functions on a compact interval
{title2=$C^\infty([0,1])$}

The space $C^\infty([0,1])$ becomes a complete metric space under
$$
d(f,g)=\sum_{r=0}^\infty2^{-r}
\min\{1,\|f^{(r)}-g^{(r)}\|_\infty\}.
$$
Convergence in this metric is exactly uniform convergence of every derivative separately.

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