The Stone-Weierstrass Theorem
G. L. M. Groenewegen, Arnoud C. M. Van Rooij · Atlantis studies in mathematics · 2016
An important result in elementary analysis is Weierstrass’ theorem, asserting that on a bounded closed interval every continuous function can be approximated uniformly by polynomial functions. We prove an extension of this result. The theorem itself lies outside our sphere of interest, but it is crucial for the representation theorems in our later chapters. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.