On and the almost-Lindelöf property

Author:
Stephen H. Hechler

Journal:
Proc. Amer. Math. Soc. **52** (1975), 353-355

MSC:
Primary 02K25; Secondary 02K05, 28A35

DOI:
https://doi.org/10.1090/S0002-9939-1975-0380706-9

MathSciNet review:
0380706

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Abstract: In 1970, Kemperman and Maharam proved that there exists a Baire measure on (where is the set of natural numbers) such that may be covered by a famliy of elementary open -null sets and used this to prove that (where is the set of real numbers) does not have the ``almost-Lindelöf'' property. We define to be the smallest cardinal for which there exists a collection of closed subsets of each of Lebesgue measure zero and which covers , and we show that in the above results can be replaced by . We then note that we have shown elsewhere that it is consistent with the negation of the continuum hypothesis that , and this, therefore, implies that it is consistent with the negation of the continuum hypothesis that not be almost-Lindelöf.

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0380706-9

Article copyright:
© Copyright 1975
American Mathematical Society