Unions of Hilbert cubes

Wong, Raymond Y. T.; Kroonenberg, Nelly

doi:10.1090/S0002-9947-1975-0377895-3

Unions of Hilbert cubes
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by Raymond Y. T. Wong and Nelly Kroonenberg

Trans. Amer. Math. Soc. 211 (1975), 289-297

DOI: https://doi.org/10.1090/S0002-9947-1975-0377895-3

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Abstract:

This paper gives a partial solution to the problem whether the union of two Hilbert cubes is a Hilbert cube if the intersection is a Hilbert cube and a Z-set in one of them. Our results imply West’s Intermediate Sum Theorem on Hilbert cube factors. Also a technique is developed to obtain Z-sets as limits of Z-sets.

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Sums of Hilbert cube factors