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Non-Complemented Open Sets in Effective Topology

  • Philip Hingston (a1)

Abstract

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.

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References

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[1]Hingston, P. F., Effectiveness in rings and topology, (Ph.D. Thesis, Monash University, 11 1983).
[2]Kalantari, I., Major subsets in effective topology. Patras Logic Symposion (Patras, 1980), pp. 7794 (Stud. Logic Foundations Math., 109, North-Holland, 1982).
[3]Kalantari, I. and Leggett, A.. ‘Simplicity in effective topology,’ J. Symbolic Logic 47 (1982), 169183.
[4]Kalantari, I. and Leggett, A., ‘Maximality in effective topology,’ J. Symbolic Logic 48 (1983), 100112.
[5]Kalantari, I. and Remmel, J. B.. Degrees of recursively enumerable topological spaces. J. Symbolic Logic 48 (1983), 610622.
[6]Kalantari, I. and Retzlaff, A.. ‘Recursive constructions in topological spaces’, J. Symbolic Logic 44 (1979), 609625.
[7]Shi, N., Unpublished abstract.
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Non-Complemented Open Sets in Effective Topology

  • Philip Hingston (a1)

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