Recursive constructions in topological spaces
- 1 December 1979
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 44 (4) , 609-625
- https://doi.org/10.2307/2273299
Abstract
We study topological constructions in the recursion theoretic framework of the lattice of recursively enumerable open subsets of a topological spaceX. 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 inX.Keywords
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