We present a constructive proof of a Stone-Weierstrass theorem for totally bounded metric spaces (SWtbms) which implies Bishop’s Stone-Weierstrass theorem for compact metric spaces (BSWcms) found in [3]. Our proof has a clear computational content, in contrast to Bishop’s highly technical proof of BSWcms and his hard to motivate concept of a (Bishop-)separating set of uniformly continuous functions. All corollaries of BSWcms in [3] are proved directly by SWtbms. We work within Bishop’s informal system of constructive mathematics BISH.
CITATION STYLE
Petrakis, I. (2016). A direct constructive proof of a stone-weierstrass theorem for metric spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9709, pp. 364–374). Springer Verlag. https://doi.org/10.1007/978-3-319-40189-8_37
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