Realcompactifications of products of ordered spaces
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- by William G. McArthur
- Proc. Amer. Math. Soc. 38 (1973), 186-192
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312470-1
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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, $\upsilon (X \times Y) = \upsilon X \times \upsilon Y$.References
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Bibliographic Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 38 (1973), 186-192
- MSC: Primary 54D60; Secondary 54F05
- DOI: https://doi.org/10.1090/S0002-9939-1973-0312470-1
- MathSciNet review: 0312470