The Steiner problem for infinitely many points
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چکیده
Let A be a given compact subset of the euclidean space. We consider the problem of finding a compact connected set S of minimal 1dimensional Hausdorff measure, among all compact connected sets containing A. We prove that when A is a finite set any minimizer is a finite tree with straight edges, thus recovery the classical Steiner Problem. Analogously, in the case when A is countable, we prove that every minimizer is a (possibly) countable union of straight segments.
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تاریخ انتشار 2009