Displaying similar documents to “Metric property of linear sets”

On a generalization of the Selection Theorem of Mahler

Gilbert Muraz, Jean-Louis Verger-Gaugry (2005)

Journal de Théorie des Nombres de Bordeaux

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The set 𝒰 𝒟 r of point sets of n , n 1 , having the property that their minimal interpoint distance is greater than a given strictly positive constant r > 0 is shown to be equippable by a metric for which it is a compact topological space and such that the Hausdorff metric on the subset 𝒰 𝒟 r , f 𝒰 𝒟 r of the finite point sets is compatible with the restriction of this topology to 𝒰 𝒟 r , f . We show that its subsets of Delone sets of given constants in n , n 1 , are compact. Three (classes of) metrics, whose one of crystallographic...