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.References
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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