On the existence of shortest networks in Banach spaces

DOI10.1134/S0001434613070043zbMath1290.46009MaRDI QIDQ382352

N. P. Strelkova, Borislav Borisovich Bednov

Publication date: 18 November 2013

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Banach spaceshortest network

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Isometric theory of Banach spaces (46B04)

Related Items (4)

The length of minimal filling for a five-point metric space ⋮ Banach spaces with shortest network length depending only on pairwise distances between points ⋮ The Steiner subratio in Banach spaces ⋮ Steiner problem in the Gromov-Hausdorff space: the case of finite metric spaces

Cites Work

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• Under a suitable renorming every nonreflexive Banach space has a finite subset without a Steiner point
• An example of nonexistence of a Steiner point in a Banach space
• Sur un théorème de Banach

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