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

Pol, Elżbieta

doi:10.1090/S0002-9939-1986-0854045-0

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

Proc. Amer. Math. Soc. 98 (1986), 349-352

DOI: https://doi.org/10.1090/S0002-9939-1986-0854045-0

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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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