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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0848898-X
PII: S 0002-9939(1986)0848898-X
Keywords: Fake $ s$-manifold, $ Z$-set, compactification
Article copyright: © Copyright 1986 American Mathematical Society