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Components of an open set

Part of: Real functions Generalities

Published online by Cambridge University Press:  09 April 2009

Mark Mandelkern
Mark Mandelkern
Affiliation:
Department of Mathematical Sciences New Mexico State University Las Cruces, New Mexico 88003, U.S.A.
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Abstract

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A classical theorem states that any open set on the real line is a countable union of disjoint open invervals. Here the numerical content of this theorem is investigated with the methods of constructive topology.

MSC classification

Secondary: 26A03: Foundations 54A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 249 - 261
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Bishop, E., Foundations of constructive analysis (McGraw-Hill, New York, 1967).Google Scholar
[2]Bridges, D. S., ‘On the connectivity of convex sets’, Bull. London Math. Soc. 10 (1978), 86–90.CrossRefGoogle Scholar
[3]Bridges, D. S., ‘More on the connectivity of convex sets’, Proc. Amer. Math. Soc. 68 (1978), 214–216.CrossRefGoogle Scholar
[4]Bridges, D. S., ‘Connectivity properties of metric spaces’, Pacific J. Math. 80 (1979), 325–331.CrossRefGoogle Scholar
[5]Mandelkern, M., ‘Connectivity of an interval’, Proc. Amer. Math. Soc. 54 (1976), 170–172.CrossRefGoogle Scholar