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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
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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$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0263053-0
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