Normality in 𝑋² for compact 𝑋

Gruenhage, G.; Nyikos, P. J.

doi:10.1090/S0002-9947-1993-1162102-5

Normality in $X^ 2$ for compact $X$
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by G. Gruenhage and P. J. Nyikos

Trans. Amer. Math. Soc. 340 (1993), 563-586

DOI: https://doi.org/10.1090/S0002-9947-1993-1162102-5

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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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