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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

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