A 2-complex is collapsible if and only if it admits a strongly convex metric
Warren White (1970)
Fundamenta Mathematicae
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Warren White (1970)
Fundamenta Mathematicae
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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.
Shaban Sedghi, Nabi Shobe, Abdelkrim Aliouche (2012)
Matematički Vesnik
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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.
Shaban Sedghi, Nguyen Van Dung (2014)
Matematički Vesnik
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B. Krakus (1972)
Fundamenta Mathematicae
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Hassen Aydi (2013)
Matematički Vesnik
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Bożena Piątek (2014)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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In this work we consider two hyperconvex diversities (or hyperconvex metric spaces) (X, δX) and (Y, δY ) with nonempty intersection and we wonder whether there is a natural way to glue them so that the new glued diversity (or metric space) remains being hyperconvex. We provide positive and negative answers in both situations.
Miheţ, Dorel (2009)
The Journal of Nonlinear Sciences and its Applications
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A. Berard, W. Nitka (1974)
Fundamenta Mathematicae
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V. W. Bryant (1970)
Compositio Mathematica
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Gajić, Ljiljana (2006)
Novi Sad Journal of Mathematics
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