Journal of Symbolic Logic

Recursive Constructions in Topological Spaces

Iraj Kalantari and Allen Retzlaff

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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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J. Symbolic Logic, Volume 44, Issue 4 (1979), 609-625.

First available in Project Euclid: 6 July 2007

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Kalantari, Iraj; Retzlaff, Allen. Recursive Constructions in Topological Spaces. J. Symbolic Logic 44 (1979), no. 4, 609--625.

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