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 | References | Similar Articles | Additional Information

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

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-96-01375-X

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