Let $V,W$ be normed spaces over $\mathbb{K}$. Let $E$ be a subset of $V$ such that each point of $E$ is a limit point of $E$.
Let $f:E\rightarrow W$ be a $C^2$ function.
Then, is it possible that $D^2f(p)(x,y)\neq D^2f(p)(y,x)$? What if $V,W$ are Euclidean spaces?
(I'm checking my proof for the case $E$ is open, but the condition $E$ is open cannot be removed in my argument)