We prove some key results about spaces of continuous functions. First we show that continuous functions on an interval can be uniformly approximated by polynomials (the Weierstrass Approximation Theorem), which has interesting applications to Fourier series. Then we prove the Stone-Weierestrass Theorem, which generalises this to continuous functions on compact metric spaces and other collections of approximating functions. We end with a proof of the Arzelà-Ascoli Theorem.
Review the options below to login to check your access.
Log in with your Cambridge Higher Education account to check access.
If you believe you should have access to this content, please contact your institutional librarian or consult our FAQ page for further information about accessing our content.