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An example of a fake $ s$-manifold with a nice locally contractible compactification

Author: Philip L. Bowers
Journal: Proc. Amer. Math. Soc. 98 (1986), 171-174
MSC: Primary 57N20; Secondary 54B17
MathSciNet review: 848898
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Abstract: An example is constructed of a topologically complete separable AR $ X$ that satisfies the discrete $ n$-cells property for each nonnegative integer $ n$ but fails to satisfy the discrete approximation property and be homeomorphic to $ s$ even though $ X$ arises as the complement of a $ \sigma $-$ Z$-set in a locally contractible compactum. Such examples are not possible in the setting of ANR compactifications.

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Keywords: Fake $ s$-manifold, $ Z$-set, compactification
Article copyright: © Copyright 1986 American Mathematical Society

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