Local compactness and Hewitt realcompactifications of products

Abstract

Abstract. In this note we prove McArthur's conjecture [6]: If card X is nonmeasurable and if v(X X Y) = vX XvY 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 X Y) = vX XvY holds.