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A complement theorem in the universal Menger compactum


Author: R. B. Sher
Journal: Proc. Amer. Math. Soc. 121 (1994), 611-618
MSC: Primary 54C50; Secondary 55P55, 57N25
DOI: https://doi.org/10.1090/S0002-9939-1994-1243173-0
MathSciNet review: 1243173
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Abstract: A. Chigogidze has shown that two Z-sets in the universal Menger compactum of dimension $ k + 1$ have the same k-shape if and only if their complements are homeomorphic. We show that this result holds for weak Z-sets. The class of weak Z-sets, defined herein and analogous to the weak Z-sets in Q, contains but is larger than the class of Z-sets. We give some examples of weak Z-sets in the universal Menger compactum and in Q that are not Z-sets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1243173-0
Keywords: Universal Menger compactum, complement theorem, Z-set, weak Z-set, shape theory, n-shape theory
Article copyright: © Copyright 1994 American Mathematical Society

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