Recursive and nonextendible functions over the reals; filter foundation for recursive analysis.II

Annals of Pure and Applied Logic 98 (1-3):87-110 (1999)

Abstract
In this paper we continue our work of Kalantari and Welch . There we introduced machinery to produce a point-free approach to points and functions on topological spaces and found conditions for both which lend themselves to effectivization. While we studied recursive points in that paper, here, we present two useful classes of recursive functions on topological spaces, apply them to the reals, and find precise accounting for the nature of the properties of some examples that exist in the literature. We end with a construction of a recursive function on a small subset of the unit interval which is strongly nonextendible
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DOI 10.1016/s0168-0072(98)00048-7
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References found in this work BETA

Nicht Konstruktiv Beweisbare Sätze der Analysis.Ernst Specker - 1949 - Journal of Symbolic Logic 14 (3):145-158.
Degrees of Recursively Enumerable Topological Spaces.Iraj Kalantari & J. B. Remmel - 1983 - Journal of Symbolic Logic 48 (3):610-622.

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Citations of this work BETA

A Blend of Methods of Recursion Theory and Topology.Iraj Kalantari & Larry Welch - 2003 - Annals of Pure and Applied Logic 124 (1-3):141-178.
On Turing Degrees of Points in Computable Topology.Iraj Kalantari & Larry Welch - 2008 - Mathematical Logic Quarterly 54 (5):470-482.

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