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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Realcompactifications of products of ordered spaces


Author: William G. McArthur
Journal: Proc. Amer. Math. Soc. 38 (1973), 186-192
MSC: Primary 54D60; Secondary 54F05
MathSciNet review: 0312470
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Abstract: The equality $ \upsilon (X \times Y) = \upsilon X \times \upsilon Y$ is studied for the case when one of the factors is a linearly ordered topological space (LOTS). Among the results obtained are the following:

1. If $ X$ is any separable realcompact space and $ Y$ is any LOTS of nonmeasurable cardinal, then $ \upsilon (X \times Y) = \upsilon X \times \upsilon Y$.

2. If $ X$ is a nonparacompact LOTS, then there is a paracompact LOTS $ Y$ such that $ \upsilon (X \times Y) \ne \upsilon X \times \upsilon Y$.

3. For any pair $ X,Y$ of well-ordered spaces, $ \upsilon (X \times Y) = \upsilon X \times \upsilon Y$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0312470-1
Keywords: Hewitt realcompactification, ordered space, product space, realcompact space
Article copyright: © Copyright 1973 American Mathematical Society