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A ZFC example (of minimum weight)
of a Lindelöf space and a completely
metrizable space with a nonnormal product


Author: L. Brian Lawrence
Journal: Proc. Amer. Math. Soc. 124 (1996), 627-632
MSC (1991): Primary 54B10; Secondary 54D20, 54E50
DOI: https://doi.org/10.1090/S0002-9939-96-02864-X
MathSciNet review: 1273506
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Abstract | References | Similar Articles | Additional Information

Abstract: We give an example as indicated in the title where the weight (i.e., the minimum cardinality of a base for the topology) of the product is the smallest uncountable cardinal.


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

  • 1 K. Alster On the product of a Lindelöf space and the space of irrationals under Martin's Axiom, Proc. Amer. Math. Soc., 110 (1990), 543--547. MR 90m:54012
  • 2 ------, Some remarks concerning the Lindelöf property of the product of a Lindelöf space with the irrationals, Topology Appl. 44 (1992), 19--25. MR 93g:54013
  • 3 K. Alster and G. Gruenhage, Remarks on the product of Lindelöf spaces (to appear).
  • 4 Amer Beslagic, Normality in products, Ann. New York Acad. Sci. 705 (1993), 17--46. MR 95f:54013
  • 5 L. B. Lawrence, The influence of a small cardinal on the product of a Lindelöf space and the irrationals, Proc. Amer. Math. Soc., 110 (1990), 535--542. MR 90m:54014
  • 6 E. A. Michael, The product of a normal space and a metric space need not be normal, Bull. Amer. Math. Soc., 69 (1963), 375--376. MR 27:2956
  • 7 ------, Paracompactness and the Lindelöf property in finite and countable cartesian products, Compositio Math., 23 (1971), 199--214. MR 44:4706
  • 8 T. C. Przymusinski, Products of normal spaces, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 781--826. MR 86c:54007

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Additional Information

L. Brian Lawrence
Affiliation: Department of Mathematics, George Mason University, Fairfax, Virginia 22030-4444

DOI: https://doi.org/10.1090/S0002-9939-96-02864-X
Keywords: Product, Lindel\"of, completely metrizable, normal, Michael line, Michael space, Continuum Hypothesis, Martin's Axiom
Received by editor(s): November 24, 1992
Received by editor(s) in revised form: March 14, 1994
Communicated by: Franklin D. Tall
Article copyright: © Copyright 1996 American Mathematical Society

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