Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T05:07:01.884Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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