NDLI: Notes on Computable Analysis

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Notes on Computable Analysis

Content Provider	Springer Nature Link
Author	Porter, Michelle Day, Adam Downey, Rodney
Copyright Year	2016
Abstract	Computable analysis has been part of computability theory since Turing’s original paper on the subject (Turing, Proc. London Math. Sc. 42:230–265, 1936). Nevertheless, it is difficult to locate basic results in this area. A first goal of this paper is to give some new simple proofs of fundamental classical results (highlighting the role of ${{\Pi }_{1}^{0}}$ classes). Naturally this paper cannot cover all aspects of computable analysis, but we hope that this gives the reader a completely self-contained ingress into this area. A second goal is to use tools from effective topology to analyse the Darboux property, particularly a result by Sierpiński, and the Blaschke Selection Theorem.
Starting Page	53
Ending Page	111
Page Count	59
File Format	PDF
ISSN	14324350
Journal	Theory of Computing Systems
Volume Number	60
Issue Number	1
e-ISSN	14330490
Language	English
Publisher	Springer US
Publisher Date	2016-12-09
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Computable analysis Computable real Computable real-valued function Markov computable Borel computable Type II computable Darboux property Blaschke Selection Theorem Convex sets Theory of Computation Computational Mathematics and Numerical Analysis
Content Type	Text
Subject	Theoretical Computer Science Computational Theory and Mathematics

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