Proceedings of the American Mathematical Society

Author(s): D. H. Fremlin; R. A. Johnson; E. Wajch
Journal: Proc. Amer. Math. Soc. 124 (1996), 2897-2903.
MSC (1991): Primary 54H05, 28A05
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Abstract: A space $X$

Borel multiplies with a space $Y$

if each Borel set of $X\times Y$ is a member of the $\sigma$ -algebra in $X\times Y$ generated by Borel rectangles. We show that a regular space $X$

Borel multiplies with every regular space if and only if $X$

has a countable network. We give an example of a Hausdorff space with a countable network which fails to Borel multiply with any non-separable metric space. In passing, we obtain a characterization of those spaces which Borel multiply with the space of countable ordinals, and an internal necessary and sufficient condition for $X$

to Borel multiply with every metric space.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 54H05, 28A05

D. H. Fremlin
Affiliation: Department of Mathematics, Essex University, Colchester C04 3SQ, England
Email: fremdh@essex.ac.uk

R. A. Johnson
Affiliation: Department of Mathematics, Washington State University, Pullman, Washington 99164
Email: johnson@beta.math.wsu.edu

E. Wajch
Affiliation: Institute of Mathematics, University of Lódz, S. Banacha 22, 90-238 Lódz, Poland
Email: ewajch@krysia.uni.lodz.pl

DOI: 10.1090/S0002-9939-96-03488-0
PII: S 0002-9939(96)03488-0
Keywords: Borel set, product $\sigma $-algebra, countable network, hereditary separability, hereditary Lindel\"{o}f property, metric space, countable ordinals
Received by editor(s): February 21, 1995
Communicated by: Franklin D. Tall
Copyright of article: Copyright 1996, American Mathematical Society

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