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.

**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