Bounded double square functions

Jill Pipher

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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...