Boundedly connected sets and the distance to the intersection of two sets |
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| Authors: | Juan-Enrique Martí nez-Legaz,Antonio Martinó n |
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| Affiliation: | a Departament d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
b Departamento de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna, Tenerife, Spain |
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| Abstract: | We prove that if (X,d) is a metric space, C is a closed subset of X and x∈X, then the distance of x to R∩S agrees with the maximum of the distances of x to R and S, for every closed subsets R,S⊂C such that C=R∪S, if and only if C is x-boundedly connected. |
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| Keywords: | Distance to the intersection Boundedly connected sets Metric spaces Normed spaces |
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