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International Journal of Modern Computation, Information and Communication Technology

ISSN 2581-5954

May-June 2021, Vol. 4, Issue 5-6, p. 25-28.​​

On the Stone-Weierstrass theorem as a vital result in the study of the algebra of continuous functions on a Compact Hausdorff space
Amos Otieno Wanjara*
Kaimosi Friends University College, Department of Mathematics and Statistics, School of Science, 

P.O BOX 385-50309, Kaimosi. Kenya.
*Corresponding author’s e-mail:
awanjara@kafuco.ac.ke

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.

Keywords: Compact space; Hausdorff space; Locally compact; Algebra; Sub-algebra; Seperability of polynomials.

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