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Note on the modified Heine-Borel Theorem
Published online by Cambridge University Press: 24 October 2008
Extract
The Heine-Borel Theorem for one-dimensional intervals may be enunciated as follows:
(A) If a set D of intervals, all in the closed interval (a, b), be such that every point of (a, b) is an interior point of at least one interval of the set D (the end points a, b being regarded as interior to an interval when either of them is an end point of such interval), then a finite set E of intervals all belonging to D exists such that every point of (a, b) is interior to at least one interval of E.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 26 , Issue 3 , July 1930 , pp. 334 - 336
- Copyright
- Copyright © Cambridge Philosophical Society 1930
References
* Cf. Carattéodory, , Vorlesungen über Reelle Funktionen (1927), 42–45.Google Scholar