A Stone-Weierstrass Type Theorem for an Unstructured Set - with Applications

摘要

A general version of the Stone-Weierstrass theorem is presented-one which involves no structure on the domain set of the real valued functions. This theorem is similar to the 'Stone-Weierstrass theorem' which appears in the book by Gillman and Jerison, but instead of involving the concept of stationary sets the one presented here involves stationary filters. As a corollary to our results we obtain Nel's theorem of Stone-Weierstrass type for an arbitrary topological space. Finally, an application is made to the setting of Cauchy spaces.