# dense subsets

• Jun 21st 2012, 04:57 PM
saravananbs
dense subsets
in $C[a,b]$, any dense subset is possible other then set of polynomials.
• Jun 22nd 2012, 12:27 AM
FernandoRevilla
Re: dense subsets
Quote:

Originally Posted by saravananbs
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.