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Non-Complemented Open Sets in Effective Topology

Part of: Generalities Computability and recursion theory

Published online by Cambridge University Press:  09 April 2009

Philip Hingston
Philip Hingston
Affiliation:
Department of Mathematics Monash University Clayton, Victoria 3168, Australia
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Abstract

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Notions of effective complementation in effective topological spaces are considered, and several types of non-complemented sets are constructed. While there are parallels with recursively enumerable sets, some unexpected differences appear. Finally, a pair of splitting theorems is proved.

MSC classification

Secondary: 03D45: Theory of numerations, effectively presented structures 54A05: Topological spaces and generalizations (closure spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 1 , February 1988 , pp. 129 - 137
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Hingston, P. F., Effectiveness in rings and topology, (Ph.D. Thesis, Monash University, 11 1983).Google Scholar
[2]Kalantari, I., Major subsets in effective topology. Patras Logic Symposion (Patras, 1980), pp. 77–94 (Stud. Logic Foundations Math., 109, North-Holland, 1982).Google Scholar
[3]Kalantari, I. and Leggett, A.. ‘Simplicity in effective topology,’ J. Symbolic Logic 47 (1982), 169–183.CrossRefGoogle Scholar
[4]Kalantari, I. and Leggett, A., ‘Maximality in effective topology,’ J. Symbolic Logic 48 (1983), 100–112.CrossRefGoogle Scholar
[5]Kalantari, I. and Remmel, J. B.. Degrees of recursively enumerable topological spaces. J. Symbolic Logic 48 (1983), 610–622.CrossRefGoogle Scholar
[6]Kalantari, I. and Retzlaff, A.. ‘Recursive constructions in topological spaces’, J. Symbolic Logic 44 (1979), 609–625.CrossRefGoogle Scholar
[7]Shi, N., Unpublished abstract.Google Scholar