Smooth function - Axioms of Choice

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Smooth function

Set

context	$X,Y$ … Banach spaces with topology
definiendum	$f\in C^\infty(X,Y)$
for all	$k\in \mathbb N$
postulate	$f\in C^k(X,Y)$
postulate	$\lim_{m\to\infty}D^mf$ … continuous

Discussion

Formalities

Here $D^mf$ denotes the $m$ th component of the sequence $Df, D^2f, D^3f,\dots$ .

Reference

Wikipedia: Differentiable function, Smooth function

Parents

Context

Differentiable function, Limit in a metric space

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