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A ZFC example (of minimum weight) of a Lindelöf space and a completely metrizable space with a nonnormal product
Author(s):
L.
Brian
Lawrence
Journal:
Proc. Amer. Math. Soc.
124
(1996),
627-632.
MSC (1991):
Primary 54B10;
Secondary 54D20, 54E50
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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:
- 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:
10.1090/S0002-9939-96-02864-X
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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