Characterizations of metric spaces by the use of their midsets: intervals
Anthony Berard (1971)
Fundamenta Mathematicae
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Anthony Berard (1971)
Fundamenta Mathematicae
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A. Lelek, Jan Mycielski (1967)
Fundamenta Mathematicae
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A. Lelek (1977)
Colloquium Mathematicae
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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.
Dickman, Raymond F.jun. (1980)
International Journal of Mathematics and Mathematical Sciences
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B. Krakus (1972)
Fundamenta Mathematicae
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A. Berard, W. Nitka (1974)
Fundamenta Mathematicae
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A. Lelek (1972)
Colloquium Mathematicae
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Borkowski, Marcin, Bugajewski, Dariusz, Phulara, Dev (2010)
Fixed Point Theory and Applications [electronic only]
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Benjamin Miesch (2015)
Analysis and Geometry in Metric Spaces
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We investigate how to glue hyperconvex (or injective) metric spaces such that the resulting space remains hyperconvex. We give two new criteria, saying that on the one hand gluing along strongly convex subsets and on the other hand gluing along externally hyperconvex subsets leads to hyperconvex spaces. Furthermore, we show by an example that these two cases where gluing works are opposed and cannot be combined.
L. F. Guseman Jr., B. C. Peters Jr. (1975)
Colloquium Mathematicae
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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.
Jack Brown (1971)
Fundamenta Mathematicae
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