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An Open Family of Sets That Have Several Minimal Fillings

Abstract

Minimal fillings of n-point metric spaces were introduced by Ivanov and Tuzhilin. It was thought that “for almost all sets” in some sense such a filling is unique. Here we introduce a counterexample to this hypothesis.

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References

  1. 1.

    A. Yu. Eremin, “A formula for the weight of a minimal filling of a finite metric space,” Mat. Sb., 204, No. 9, 51–72 (2013).

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    A. O. Ivanov and A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem,” Sb. Math., 203, No. 5, 677–726 (2012).

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Correspondence to Z. Ovsyannikov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 153–156, 2013.

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Ovsyannikov, Z. An Open Family of Sets That Have Several Minimal Fillings. J Math Sci 203, 855–857 (2014). https://doi.org/10.1007/s10958-014-2176-5

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Keywords

  • Russia
  • Software Package
  • Continuous Function
  • Distance Matrix
  • Open Family