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Chapter 5 Uniform Approximation
Consider the following uniform approximation problem for continuous functions. Suppose that \(a, b \in \R\) with \(a \lt b\text{.}\) Given a function \(f \in C^0([a,b])\text{,}\) is it possible to approximate \(f\) by ‘nice’ functions, say, by polynomials with real coefficients? If so, we may be able to prove certain statements about continuous functions by considering just polynomials.
