Question
Let S = \{(x,y) \in \mathbb{R}^2\,:\,x\in[0,\pi],\,y\in[0,1]\}. Deduce whether or not,
\left\{\sum_{m,n=0}^M a_{m,n}\cos(mx)y^n\,:\,a_{m,n} \in \mathbb{R}\right\}
a subset of C(S,\mathbb{R}) is dense.
I was thinking no. And this is not a guess.
My reasoning is as...