Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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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Keywords: Union of Hilbert cubes, union of Hilbert cube factors, cap set, fd cap set, inverse limit, near homeomorphism, $ {G_\delta }$ in hyperspace
Article copyright: © Copyright 1975 American Mathematical Society