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It would be extremely helpful if someone can suggest foundational textbooks on Recursive Analysis (Computability over Reals) which explains connections between Computability and the Topological properties of continuous sets. I could not find any, except "Recursive Analysis" by R.L. Goodstein but I dont have any feedback on that book. I would also like to ask for suggestions regarding a book on Complexity over Real Numbers which again deals with the connection between the complexity and the topology of a set. The only book I found on the net was "Complexity and Real Computation" by Lenore Blum et al but I am not sure if that is the book which I am looking for. Thanks in advance.

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There are some good books - 1. Computable Analysis - Pour-El and Richards (an older reference) 2. Computable Analysis - Weihrauch

There's also the Blum-Shub-Smale Model, which is the model explored in "Complexity and Real Computation".

The complexity theory of computability of reals is explored in 1. Computational Complexity of real functions - Ker-I Ko

A regular conference which explores this area is "Computability and Complexity in Analysis", held annually.

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The website of Computability and Complexity in Analysis Network has extensive bibliography. See their page for books.

For computability, see

It also has a chpater on complexity.

See also PhD theses of Jens Blanc and Andrej Bauer.

Another interesting paper is

  • Viggo Stoltenberg-Hansen and John Tucker, "Computability on Topological Spaces via Domain Representations", 1997.
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