A Characterization of the Least Cardinal for which the Baire Category Theorem Fails

Arnold W. Miller

Type: Article

Publication Date: 1982-11-01

Citations: 12

DOI: https://doi.org/10.2307/2044457

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 $\kappa$.

Locations

Proceedings of the American Mathematical Society - View - PDF

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