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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A weakly infinite-dimensional space whose product with the irrationals is strongly infinite-dimensional


Author: Elżbieta Pol
Journal: Proc. Amer. Math. Soc. 98 (1986), 349-352
MSC: Primary 54F45; Secondary 54B10
MathSciNet review: 854045
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Abstract: We give an example of a weakly infinite-dimensional space $ X$ such that the product $ X \times B$ of $ X$ and a subspace $ B$ of the irrationals is strongly infinite-dimensional; under the assumption of the Continuum Hypothesis, $ B$ can be the irrationals. This example answers a question of Addis and Gresham [AG].


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0854045-0
PII: S 0002-9939(1986)0854045-0
Keywords: Weakly infinite-dimensional spaces, products, property $ C$
Article copyright: © Copyright 1986 American Mathematical Society