A Direct Constructive Proof of a Stone-Weierstrass Theorem for Metric Spaces

Petrakis, Iosif (2016): A Direct Constructive Proof of a Stone-Weierstrass Theorem for Metric Spaces. In: Beckmann, Arnold; Bienvenu, Laurent; Jonoska, Nataša (eds.) : Pursuit of the Universal. 12th Conference on Computability in Europe, CiE 2016, Paris, France, June 27 - July 1, 2016, Proceedings. Theoretical Computer Science and General Issues, Vol. 9709. Cham: Springer. pp. 364-374

Abstract

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.

• Item Type: Book Section
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISBN: 978-3-319-40188-1; 978-3-319-40189-8
• Place of Publication: Cham
• Language: English