Recursive constructions in topological spaces

Journal of Symbolic Logic 44 (4):609-625 (1979)
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Abstract

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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References found in this work

Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.
General Topology.John L. Kelley - 1962 - Journal of Symbolic Logic 27 (2):235-235.
Recursively enumerable vector spaces.G. Metakides - 1977 - Annals of Mathematical Logic 11 (2):147.
Automorphisms of the Lattice of Recursively Enumerable Vector Spaces.Iraj Kalantari - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (25-29):385-401.
Automorphisms of the Lattice of Recursively Enumerable Vector Spaces.Iraj Kalantari - 1979 - Mathematical Logic Quarterly 25 (25‐29):385-401.

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