Unions of Hilbert cubes

Authors:
Raymond Y. T. Wong and Nelly Kroonenberg

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

MSC:
Primary 57A20; Secondary 54B10, 54F40

MathSciNet review:
0377895

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

Keywords:
Union of Hilbert cubes,
union of Hilbert cube factors,
cap set,
fd cap set,
inverse limit,
near homeomorphism,
in hyperspace

Article copyright:
© Copyright 1975
American Mathematical Society