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Note on the modified Heine-Borel Theorem

Published online by Cambridge University Press:  24 October 2008

S. Verblunsky
Affiliation:
Magdalene College

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
Copyright
Copyright © Cambridge Philosophical Society 1930

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References

* Cf. Carattéodory, , Vorlesungen über Reelle Funktionen (1927), 4245.Google Scholar