Minimal parametric networks in hyperspaces are nontrivial only in finiteness classes where all Hausdorff distances are finite, with interior vertices corresponding to Fermat-Steiner solutions and generalized conditions for one-sided distances on convex sets.
North–Holland (1992)
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Minimal Parametric Networks in Hyperspaces and their Properties
Minimal parametric networks in hyperspaces are nontrivial only in finiteness classes where all Hausdorff distances are finite, with interior vertices corresponding to Fermat-Steiner solutions and generalized conditions for one-sided distances on convex sets.