An example of an infinite Steiner tree connecting an uncountable set
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Abstract
We construct an example of a Steiner tree with an infinite number of branching points connecting an uncountable set of points. Such a tree is proven to be the unique solution to a Steiner problem for the given set of points. As a byproduct we get the whole family of explicitly defined finite Steiner trees, which are unique connected solutions of the Steiner problem for some given finite sets of points, and with growing complexity (i.e. the number of branching points).
Funding source: St. Petersburg State University
Award Identifier / Grant number: #6.38.670.2013
Funding source: St. Petersburg State University
Award Identifier / Grant number: #6.38.223.2014
Funding source: Russian Government
Award Identifier / Grant number: NSh-1771.2014.1
Funding source: GNAMPA
Funding source: RFBR
Award Identifier / Grant number: #14-01-00534
Funding source: Italian Ministry of Research
Award Identifier / Grant number: 2010A2TFX2 “Calcolo delle variazioni”
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