Recursive constructions in topological spaces

Journal of Symbolic Logic 44 (4):609-625 (1979)
We study topological constructions in the recursion theoretic framework of the lattice of recursively enumerable open subsets of a topological space X. Various constructions produce complemented recursively enumerable open sets with additional recursion theoretic properties, as well as noncomplemented open sets. In contrast to techniques in classical topology, we construct a disjoint recursively enumerable collection of basic open sets which cannot be extended to a recursively enumerable disjoint collection of basic open sets whose union is dense in X
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DOI 10.2307/2273299
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References found in this work BETA
Recursively Enumerable Vector Spaces.G. Metakides & A. Nerode - 1977 - Annals of Mathematical Logic 11 (2):147-171.

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Effective Topological Spaces I: A Definability Theory.Iraj Kalantari & Galen Weitkamp - 1982 - Annals of Pure and Applied Logic 29 (1):1-27.
Effective Topological Spaces II: A Hierarchy.Iraj Kalantari & Galen Weitkamp - 1982 - Annals of Pure and Applied Logic 29 (2):207-224.
Effective Topological Spaces III: Forcing and Definability.Iraj Kalantari & Galen Weitkamp - 1987 - Annals of Pure and Applied Logic 36 (1):17-27.
Effective Inseparability in a Topological Setting.Dieter Spreen - 1996 - Annals of Pure and Applied Logic 80 (3):257-275.

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