Abstract
A. Chigogidze has shown that two Z-sets in the universal Menger compactum of dimension k + 1 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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