Notes on Computable Analysis
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 Π10${{\Pi }_{1}^{0}}$ 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.