Hi,

how to prove, that for $\displaystyle n=1$ and $\displaystyle \Omega:=(0,1)$ the embedding $\displaystyle C^0(\overline{\Omega}) \to L^2(\Omega)$ is not compact?

I've got a hint, to use the sequence $\displaystyle f_k(x)=\sin(\pi k x)$ with $\displaystyle k \in \mathbb N$. So, I should prove, that the space is not sequentially compact.

Please can you help me?

Bye,

Alexander