dense subsets

**saravananbs** · June 21st 2012, 04:57 PM

in $C[a,b]$ , any dense subset is possible other then set of polynomials.

**FernandoRevilla** · June 22nd 2012, 12:27 AM

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.

Thread: dense subsets

LinkBack

Thread Tools

Display

dense subsets

Re: dense subsets

Similar Math Help Forum Discussions

if A is an open subset of R, then A is dense if and only if R - A is nowhere dense

Continuous Mappings of Dense subsets

Prove that the Image of a Continuous Function on a Dense Set is Dense

Nowhere Dense

dense

Search Tags