Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 2 down vote favorite

Can manifolds be uniformly approximated by varieties in the way that continuous functions can be uniformly approximated by polynomials?

I got the idea from reading the Princeton companion to mathematics when it gave:

Theorem (Nash) Let M be a manifold in $\mathbb{R}^n$. Fix any large number R. Then there is a polynomial f whose zero set is as close to M as we want, at least inside a ball of radius R around the origin.

share|improve this question
2  
What do you mean by "in the way that..." ? Given a manifold what would you like an approximation to it to mean? – Ryan Budney Mar 5 '11 at 0:52
My idea is very fuzzy. I don't know in what way or what type of approximation. – user7769 Mar 5 '11 at 0:59
Do you only care about smooth manifolds or are $C^k$-manifolds also fine? – Gerben Mar 7 '11 at 19:48

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.