Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57N20, 54B17

Retrieve articles in all journals with MSC: 57N20, 54B17

Additional Information

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

American Mathematical Society