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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Relationships between continuum neighborhoods in inverse limit spaces and separations in inverse limit sequences
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by Harvey S. Davis PDF
Proc. Amer. Math. Soc. 64 (1977), 149-153 Request permission

Abstract:

The main result of this paper is the following theorem. Let $\{ {X_\alpha },{f_{\alpha \beta }},\alpha ,\beta \in I\}$ be an inverse system of compact Hausdorff spaces and continuous onto maps with inverse limit X. Let $p \in X$ and A be closed in X. There exists a continuum neighborhood of p disjoint from A if and only if there exists $\alpha \in I$ and disjoint sets U and V open in ${X_\alpha }$, neighborhoods respectively of ${p_\alpha }$ and ${A_\alpha }$ such that for all $\beta \geqslant \alpha ,f_{\alpha \beta }^{ - 1}(U)$ lies in a single component of ${X_\beta } - f_{\alpha \beta }^{ - 1}(V)$. This is Theorem B of the text.
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 149-153
  • MSC: Primary 54B25; Secondary 54F20
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0442876-5
  • MathSciNet review: 0442876