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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Local compactness and Hewitt realcompactifications of products


Author: Haruto Ohta
Journal: Proc. Amer. Math. Soc. 69 (1978), 339-343
MSC: Primary 54D60
MathSciNet review: 0482673
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Abstract: In this note we prove McArthur's conjecture [6]: If card X is nonmeasurable and if $ v(X \times Y) = vX \times vY$ holds for each space Y, then X is locally compact. Consequently, we can completely characterize the class of all spaces X such that for each space Y, $ v(X \times Y) = vX \times vY$ holds.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0482673-9
PII: S 0002-9939(1978)0482673-9
Keywords: Hewitt realcompactification, realcompact space, locally compact space, locally pseudocompact space, k-space, product space, topological completion
Article copyright: © Copyright 1978 American Mathematical Society