This article is cited in 7 papers

On the Existence of Shortest Networks in Banach Spaces

B. B. Bednov, N. P. Strelkova

M. V. Lomonosov Moscow State University

Abstract: For dual spaces, and also for $L_1$, it is proved that every system of points in such a space admits a shortest network connecting the points. An example of a Banach space is presented in which, for every $n\ge 3$, there is a system of $n$ points which cannot be connected by a shortest network.

Keywords: Banach space, networks connecting given points, shortest network.

UDC: 517.982.256+515.124.4

Received: 09.06.2011
Revised: 19.11.2012

DOI: 10.4213/mzm9228

 English version: Mathematical Notes, 2013, 94:1, 41–48

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