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Relations between concentrated sets and sets possessing property C

Published online by Cambridge University Press:  24 October 2008

A. S. Besicovitch
A. S. Besicovitch
Affiliation:
Trinty CollegeCambridge
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Extract

1. Definition 1. A linear set E is said to possess the property C if, to any sequence of positive numbers {ln} (n = 1, 2, …), there corresponds a set of intervals, of length not greater than l1, l2, …, which includes all the points of E.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 38 , Issue 1 , January 1942 , pp. 20 - 23
Copyright
Copyright © Cambridge Philosophical Society 1942

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References

* Sierpínski, W., ‘Hypothèse du continu’, Monografie Matematyczne, M4 (Warszawa-Lwów, 1934)Google Scholar. Besicovitch, A. S., ‘Concentrated and rarified sets of points’, Acta Math. 62 (1934), 289CrossRefGoogle Scholar. A thorough investigation of the property C and of allied problems is given in Rothberger, F., ‘Sur les families indénombrables des suites de nombres naturels et les problèmes concernant la propriété C’, Proc. Cambridge Phil. Soc. 37 (1941), 109.CrossRefGoogle Scholar

† ‘Remarque sur le problème de l'invariance topologique de la propriété C’, Fund. Math. 30 (1938), 56.Google Scholar