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

 

A characterization of the connectivity of a manifold in terms of large open cells


Author: R. Richard Summerhill
Journal: Proc. Amer. Math. Soc. 45 (1974), 285-290
MSC: Primary 57A60
MathSciNet review: 0380808
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Abstract: If $ k$ and $ n$ are integers, $ 0 \leqslant k \leqslant n - 3$, and $ {M^n}$ is a topological $ n$-manifold without boundary, it is shown that $ M$ is $ k$-connected if and only if there is a ``tame'' $ (n - k - 1)$-dimensional closed subset $ X$ in $ M$ such that $ M - X$ is homeomorphic to $ {E^n}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0380808-6
PII: S 0002-9939(1974)0380808-6
Article copyright: © Copyright 1974 American Mathematical Society