ON WEIERSTRASS-STONE THEOREM FOR ALGEBRAS AND MODULES OF CONTINUOUS FUNCTIONS

Document Type : Research and Reference

Author

Department of mathematics, Faculty of Sciences, King Abdel Aziz University, P. O. Box 30305, Jeddah 21477, Saudi Arabia

Abstract

This paper studies from the viewpoint of vector fibrations and vector spaces of cross-sections, endowed with appropriate topologies, the realm of ideas and results centered around the Weierstrass-Stone Theorem for algebras and modules of continuous functions in the real and self-adjoint complex cases. The proof of the equivalence between the separating and the general cases of such results by means of a quotient construction motivate the use of vector fibrations.

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