Local compactness and Hewitt realcompactifications of products

Ohta, Haruto

doi:10.1090/S0002-9939-1978-0482673-9

Local compactness and Hewitt realcompactifications of products
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Proc. Amer. Math. Soc. 69 (1978), 339-343 Request permission

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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