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 |
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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 |
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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 |
ID Code: | 47336 |
Deposited On: | 27. Apr 2018 08:12 |
Last Modified: | 04. Nov 2020 13:24 |
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