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Transactions of the American Mathematical Society

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The product of two normal initially $ \kappa$-compact spaces


Author: Eric K. van Douwen
Journal: Trans. Amer. Math. Soc. 336 (1993), 509-521
MSC: Primary 54B10; Secondary 03E35, 03E50, 54A35, 54D20, 54D35
DOI: https://doi.org/10.1090/S0002-9947-1993-1022170-8
MathSciNet review: 1022170
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that it is independent from $ {\text{ZFC}}$ that for every cardinal $ \kappa $ the following statements are equivalent:

(a) $ \kappa $ is singular;

(b) initial $ \kappa $-compactness (defined above the introduction) is productive;

(c) initial $ \kappa $-compactness is finitely productive; and

(d) the product of two initially $ \kappa $-compact normal spaces is initially $ \kappa $-compact.

In particular, MA$ $ implies that there are two countably compact normal spaces whose product is not countably compact.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1022170-8
Keywords: Initially $ \kappa $-compact, generalized $ \Sigma $-product, countably compact, $ {\text{GCH}}$, normal, $ {\text{MA}}$, product, regular cardinal, compactification
Article copyright: © Copyright 1993 American Mathematical Society

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