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Currently displaying 1 – 2 of 2

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On a generalization of the Selection Theorem of Mahler

Gilbert Muraz; Jean-Louis Verger-Gaugry — 2005

Journal de Théorie des Nombres de Bordeaux

The set $𝒰 𝒟_{r}$ of point sets of $ℝ^{n}, n \geq 1$ , 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 $𝒰 𝒟_{r, f} \subset 𝒰 𝒟_{r}$ 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 $ℝ^{n}, n \geq 1$ , are compact. Three (classes of) metrics, whose one of crystallographic nature,...

Compact multipliers. (Multiplicateurs compacts.)

Muraz, Gilbert — 1997

Bulletin of the Belgian Mathematical Society - Simon Stevin

Page 1

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