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On the Property С and A Problem of Hausdorff

Published online by Cambridge University Press:  20 November 2018

Fritz Rothberger
Fritz Rothberger*
Affiliation:
University of New Brunswick
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In an earlier paper [3] I studied the property С and related properties С′ and С; but the principal problem, viz, to prove, with the axiom of choice only (without any other hypothesis), the existence of a nondenumerable set of property С, remains open.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 111 - 116
Copyright
Copyright © Canadian Mathematical Society 1952

References

1. Hausdorff, F., Summen von Mengen, Fund. Math., vol. 26 (1936), 247.Google Scholar
2. Rothberger, F., Eine Verscharfung der Eigenschaft C, Fund. Math., vol. 30 (1938), 54.Google Scholar
3. Rothberger, F., Sur les familles indénombrables de suites de nombres naturels et les problémes concernant la propriété G, Proc. Cambridge Philos. Soc, vol. 37 (1941), 109–126.Google Scholar
4. Rothberger, F., On some problems of Hausdorff and of Sierpinski, Fund. Math., vol. 35 (1948), 29–46.Google Scholar