A Characterization of the Least Cardinal for which the Baire Category Theorem Fails
Arnold W. Miller
Proceedings of the American Mathematical Society, Vol. 86, No. 3. (Nov., 1982), pp. 498-502.
AbstractLet $\kappa$ 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 $\kappa$.