It is proved, within Bishop's constructive mathematics (BISH), that, in the context of a Hilbert space, the Open Mapping Theorem is equivalent to a principle that holds in intuitionistic mathematics and recursive constructive mathematics but is unlikely to be provable within BISH.
A General Constructive Intermediate Value Theorem
β Scribed by Douglas S. Bridges
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 180 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
β¦ Synopsis
Proof. We first prove the paraconvexity of u ( X ) . Consider a, 6 , and y such that u(a) 5 y 5 u(b), and let E > 0. We use an approximate "approximate interval-28 Ztschr. f. math. Logik
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