Some properties of convex metric spaces
B. Krakus (1972)
Fundamenta Mathematicae
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B. Krakus (1972)
Fundamenta Mathematicae
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Taras Banakh, Ivan Hetman (2011)
Studia Mathematica
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We prove that a closed convex subset C of a complete linear metric space X is polyhedral in its closed linear hull if and only if no infinite subset A ⊂ X∖ C can be hidden behind C in the sense that [x,y]∩ C ≠ ∅ for any distinct x,y ∈ A.
Tulsi Dass Narang (1981)
Archivum Mathematicum
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Alireza Moazzen, Yoel-Je Cho, Choonkil Park, Madjid Eshaghi Gordji (2017)
Mathematica Bohemica
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Tadeusz Dobrowolski, Jan van Mill (2006)
Fundamenta Mathematicae
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We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
V. W. Bryant (1970)
Compositio Mathematica
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Tadeusz Rzeżuchowski (2012)
Open Mathematics
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We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.
Huynh Van Ngai, Jean-Paul Penot (2008)
Studia Mathematica
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We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded....
Ismat Beg (2003)
Czechoslovak Mathematical Journal
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We obtain necessary conditions for convergence of the Cauchy Picard sequence of iterations for Tricomi mappings defined on a uniformly convex linear complete metric space.
Tadeusz Dobrowolski (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.