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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of the least cardinal for which the Baire category theorem fails


Author: Arnold W. Miller
Journal: Proc. Amer. Math. Soc. 86 (1982), 498-502
MSC: Primary 04A15; Secondary 03E05, 54H05
DOI: https://doi.org/10.1090/S0002-9939-1982-0671224-2
MathSciNet review: 671224
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Abstract: Let $ \kappa $ be the least cardinal such that the real line can be covered by $ \kappa $ many nowhere dense sets. We show that $ \kappa $ can be characterized as the least cardinal such that "infinitely equal" reals fail to exist for families of cardinality $ \kappa $.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0671224-2
Article copyright: © Copyright 1982 American Mathematical Society