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

Miller, Arnold W.

doi:10.1090/S0002-9939-1982-0671224-2

A characterization of the least cardinal for which the Baire category theorem fails
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Proc. Amer. Math. Soc. 86 (1982), 498-502 Request permission

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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