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Failure of normality in the box product of uncountably many real lines

Authors:	L Brian Lawrence

Institution:	Department of Mathematics, George Mason University, Fairfax, Virginia 22030-4444

Abstract:	We prove in ZFC that the box product of $\omega_1$ many copies of $\omega+1$ is neither normal nor collectionwise Hausdorff. As an addendum to the proof, we show that if the cardinality of the continuum is $2^{\omega_1}$ , then these properties also fail in the closed subspace consisting of all functions which assume the value $\omega$ on all but countably many indices.

Keywords:	Box product normal paracompact collectionwise Hausdorff continuum hypothesis

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