On the Stone-Weierstrass theorem as a vital result in the study of the algebra of continuous functions on a Compact Hausdorff space

Abstract

In this paper, we present the different versions and formulations of the Stone- Weierstrass theorem that makes it a vital result in the study of the algebra of continuous functions on a compact Hausdorff space. Instead of the real interval [a,b], an arbitrary compact Hausdorff space X is considered and instead of the algebra of polynomial functions, approximation with elements from more general sub-algebras of C(X) is considered. Some of its contributions and impact to the study of the algebra of continuous functions are also highlighted.