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Transactions of the American Mathematical Society

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

Author: L. Brian Lawrence
Journal: Trans. Amer. Math. Soc. 348 (1996), 187-203
MSC (1991): Primary 54D18; Secondary 54A35, 54B10, 54B20
MathSciNet review: 1303123
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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.

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Additional Information

Keywords: Box product, normal, paracompact, collectionwise Hausdorff, continuum hypothesis
Received by editor(s): November 22, 1991
Received by editor(s) in revised form: October 31, 1994
Additional Notes: An abstract of this paper was presented at the Summer Topology Conference in Honor of Mary Ellen Rudin, University of Wisconsin, Madison, June, 1991
Dedicated: Dedicated to Mary Ellen Rudin and A. H. Stone
Article copyright: © Copyright 1996 American Mathematical Society

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