My question is simple: how is the space of $C^k$ functions defined for any $k\in\mathbb R$
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$k$ times continuously differentiable functions – infinity Feb 25 '20 at 18:36
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http://mathworld.wolfram.com/C-kFunction.html – PinkyWay Feb 25 '20 at 18:37
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@infinity: Note that the the question says any real $k$, not necessarily a nonnegative integer. – Hans Lundmark Feb 25 '20 at 19:49
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For $k\in\mathbb{R}_{>0}$ see https://math.stackexchange.com/q/3324620/169085 (with $k=q+\alpha$). – Alp Uzman May 16 '22 at 03:10