Boundedly connected sets and the distance to the intersection of two sets

Juan Enrique Martínez-Legaz, Antonio Martinón

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

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. © 2006 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)400-406
JournalJournal of Mathematical Analysis and Applications
Volume332
DOIs
Publication statusPublished - 1 Aug 2007

Keywords

  • Boundedly connected sets
  • Distance to the intersection
  • Metric spaces
  • Normed spaces

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