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Recursive constructions in topological spaces

Published online by Cambridge University Press:  12 March 2014

Iraj Kalantari  and
Allen Retzlaff
Iraj Kalantari
Affiliation:
University of California, Santa Barbara, California 93106
Allen Retzlaff
Affiliation:
Western Illinois University, Macomb, Illinois 61455 State University of New York, Purchase, New York 10577
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 44 , Issue 4 , December 1979 , pp. 609 - 625
Copyright
Copyright © Association for Symbolic Logic 1979

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References

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