I asked a question on clarification of the symbol $C^k$. It was confirmed to me that $C^k$ is actually a space of functions. Now my next question in the definition is on $C^0$ and $C^1$.
$C^0$ is ok to me as a space of continuous but it beat my imagination how $C^1$ is defined as a space of continuously differentiable functions. Shouldn't $C^1$ just mean the space of functions with at least first derivative? To me from the way it is defined at mathworld web site, $k=0$ or $k=1$. Thus, $C^k$ is just twice continuously differentiable! Please let somebody clarify.
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$\begingroup$$C^1$ means space of those function whose first derivative along with itself is continuous (it may have several other derivatives but they do not have to be continuous) on whatever domain you are working in.
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