in $C[a,b]$, any dense subset is possible other then set of polynomials.
in $C[a,b]$, any dense subset is possible other then set of polynomials.
Yes, the algebra generated by $\mathcal{F}=\{e^{nx}:n\in\mathbb{Z}\}$ contains the constant functions and separate points. Now, use the Stone-Weierstrass theorem.