Doignon’s theorem

Target entity: Doignon’s theorem
Context triple: [Helly’s theorem, hasVariant, Doignon’s theorem]

• A. Helly’s theorem
  Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
• B. Radon’s theorem
  Radon’s theorem is a fundamental result in convex geometry stating that any set of sufficiently many points in Euclidean space can be partitioned into two disjoint subsets whose convex hulls intersect.
• C. Low’s theorem
  Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
• D. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• E. Jarník–Besicovitch theorem
  The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Doignon’s theorem
Target entity description: Doignon’s theorem is a discrete analogue of Helly’s theorem that characterizes when a family of convex sets in Euclidean space has an integer point in common based on the intersections of small subfamilies.

• A. Helly’s theorem
  Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
• B. Radon’s theorem
  Radon’s theorem is a fundamental result in convex geometry stating that any set of sufficiently many points in Euclidean space can be partitioned into two disjoint subsets whose convex hulls intersect.
• C. Low’s theorem
  Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
• D. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• E. Jarník–Besicovitch theorem
  The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
• F. None of above. chosen