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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Characterization of finite-dimensional $ Z$-sets


Author: Nelly Kroonenberg
Journal: Proc. Amer. Math. Soc. 43 (1974), 421-427
MSC: Primary 57A20; Secondary 54F35
DOI: https://doi.org/10.1090/S0002-9939-1974-0334221-8
MathSciNet review: 0334221
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Abstract: It is proved that closed finite-dimensional subsets of $ Q$ and $ {l_2}$ are $ Z$-sets iff their complement is $ 1$-ULC. As a corollary, closed finite-dimensional sets of deficiency 1 are shown to be $ Z$-sets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0334221-8
Keywords: Hilbert cube, Hilbert space, finite-dimensional $ Z$-set, $ 1$-ULC, homology, Alexander duality theorem, Hurewicz theorem
Article copyright: © Copyright 1974 American Mathematical Society