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Transactions of the American Mathematical Society

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Countable box products of ordinals


Author: Mary Ellen Rudin
Journal: Trans. Amer. Math. Soc. 192 (1974), 121-128
MSC: Primary 04A10; Secondary 54B10, 54D15
DOI: https://doi.org/10.1090/S0002-9947-1974-0340022-1
MathSciNet review: 0340022
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Abstract: The countable box product of ordinals is examined in the paper for normality and paracompactness. The continuum hypothesis is used to prove that the box product of countably many $ \sigma $-compact ordinals is paracompact and that the box product of another class of ordinals is normal. A third class trivially has a nonnormal product.


References [Enhancements On Off] (What's this?)

  • [1] M. E. Rudin, A normal space X such that $ X \times I$ is not normal, Fund. Math. 73 (1971) 179-186.
  • [2] Mary Ellen Rudin, The box product of countably many compact metric spaces, General Topology and Appl. 2 (1972), 293–298. MR 0324619

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0340022-1
Keywords: Product, box product, continuum hypothesis, paracompact, normal, $ \mathcal{O}$-compact
Article copyright: © Copyright 1974 American Mathematical Society

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