Porosity results for two-set nearest and farthest point problems

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• 作者：Wissam Boulos ; Simeon Reich
• 关键词：Banach space ; Complete metric space ; Farthest points ; Geodesic space ; Nearest points ; Porous set ; 41A65 ; 54E35 ; 54E52
• 刊名：Rendiconti del Circolo Matematico di Palermo
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：64
• 期：3
• 页码：493-507
• 全文大小：439 KB
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• 作者单位：Wissam Boulos (1)
  Simeon Reich (1)
  
  1. Department of Mathematics, The Technion 鈥?Israel Institute of Technology, 32000, Haifa, Israel
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Geometry
  Analysis
  Applications of Mathematics
  
• 出版者：Springer Milan
• ISSN：1973-4409

文摘

Given two nonempty, closed and bounded subsets A and B of a complete geodesic space \((X,\rho ,M)\), we consider the problems of finding pairs of nearest and farthest points in A and B. Denoting by B(X) the family of all nonempty, closed and bounded subsets of X, we first endow \(B(X) \times B(X)\) with a pair of natural metrics. We then define corresponding metric spaces \({\mathcal {M}}\) of pairs (A, B) and construct subsets \(\Omega \) of \({\mathcal {M}}\) with \(\sigma \)-porous complements such that for each pair in \(\Omega \), these problems are well posed. Keywords Banach space Complete metric space Farthest points Geodesic space Nearest points Porous set