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)


Approximating residual sets by strongly residual sets

Author: D. A. Moran
Journal: Proc. Amer. Math. Soc. 25 (1970), 752-754
MSC: Primary 54.78
MathSciNet review: 0263053
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a closed topological manifold, $ R$ residual in $ M$, and $ N$ any neighborhood of $ R$ in $ M$. The fulfillment by $ R$ of a certain local separation property in $ M$ implies that there exists a topological spine $ R'$ of $ M$ such that $ N \supset R' \supset R$. (Topological spine = strongly residual set.) This local separation property is satisfied whenever $ R$ is an $ \operatorname{ANR} $, or when $ \dim R \leqq \dim M - 2$.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.78

Retrieve articles in all journals with MSC: 54.78

Additional Information

PII: S 0002-9939(1970)0263053-0
Keywords: Topological manifold, residual set, strongly residual, topological spine, Brown-Casler map
Article copyright: © Copyright 1970 American Mathematical Society