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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Normality in $ X\sp 2$ for compact $ X$


Authors: G. Gruenhage and P. J. Nyikos
Journal: Trans. Amer. Math. Soc. 340 (1993), 563-586
MSC: Primary 54A35; Secondary 54D15, 54D30
MathSciNet review: 1162102
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Abstract: In 1977, the second author announced the following consistent negative answer to a question of Katětov: Assuming $ {\text{MA}} + \neg {\text{CH}}$, there is a compact nonmetric space $ X$ such that $ {X^2}$ is hereditarily normal. We give the details of this example, and construct another example assuming $ {\text{CH}}$. We show that both examples can be constructed so that $ {X^2}\backslash \Delta $ is perfectly normal. We also construct in $ {\text{ZFC}}$ a compact nonperfectly normal $ X$ such that $ {X^2}\backslash \Delta $ is normal.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1162102-5
PII: S 0002-9947(1993)1162102-5
Article copyright: © Copyright 1993 American Mathematical Society