Failure of normality in the box product of uncountably many real lines
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- by L. Brian Lawrence PDF
- Trans. Amer. Math. Soc. 348 (1996), 187-203 Request permission
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.References
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Additional Information
- 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
- © Copyright 1996 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 348 (1996), 187-203
- MSC (1991): Primary 54D18; Secondary 54A35, 54B10, 54B20
- DOI: https://doi.org/10.1090/S0002-9947-96-01375-X
- MathSciNet review: 1303123
Dedicated: Dedicated to Mary Ellen Rudin and A. H. Stone