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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Approximating residual sets by strongly residual sets
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by D. A. Moran
Proc. Amer. Math. Soc. 25 (1970), 752-754
DOI: https://doi.org/10.1090/S0002-9939-1970-0263053-0

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
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Bibliographic Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 25 (1970), 752-754
  • MSC: Primary 54.78
  • DOI: https://doi.org/10.1090/S0002-9939-1970-0263053-0
  • MathSciNet review: 0263053