Necessary and sufficient conditions for hyperplane transversals
By applying the Borsuk-Ulam theorem the authors prove that a family of compact connected sets in \({\mathbb{R}}^ d\) has a hyperplane transversal if and only if for some \(k\in [0,d-1]\) there is a non-trivial k-ordering of the family such that every \(k+2\) sets are intersected by some oriented k- flat consistent with the k-ordering.
family of compact connected sets in \({\mathbb{R}}^ d\)
scientific article; zbMATH DE number 4190573