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Proceedings of the American Mathematical Society

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

 
 

 

Equidistant sets and their connectivity properties


Author: J. B. Wilker
Journal: Proc. Amer. Math. Soc. 47 (1975), 446-452
DOI: https://doi.org/10.1090/S0002-9939-1975-0355791-0
MathSciNet review: 0355791
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Abstract | References | Additional Information

Abstract: If $ A$ and $ B$ are nonvoid subsets of a metric space $ (X,d)$, the set of points $ x \in X$ for which $ d(x,A) = d(x,B)$ is called the equidistant set determined by $ A$ and $ B$. Among other results, it is shown that if $ A$ and $ B$ are connected and $ X$ is Euclidean $ n$-space, then the equidistant set determined by $ A$ and $ B$ is connected.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355791-0
Keywords: Equidistant set, metric space, Euclidean $ n$-space connected set, Baire category, Mayer-Vietoris sequence
Article copyright: © Copyright 1975 American Mathematical Society

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