Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57A60

Retrieve articles in all journals with MSC: 57A60

Additional Information

PII: S 0002-9939(1974)0380808-6
Article copyright: © Copyright 1974 American Mathematical Society