Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Helly's theorem | Statement: [Knaster–Kuratowski–Mazurkiewicz lemma, relatedTo, Helly's theorem]

Target entity: Helly's theorem
Context triple: [Knaster–Kuratowski–Mazurkiewicz lemma, relatedTo, Helly's theorem]

• A. Helly’s theorem chosen
  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. colorful Helly theorem
  The colorful Helly theorem is a combinatorial geometric result that generalizes Helly’s theorem by asserting intersection properties for families of convex sets partitioned into color classes.
• C. fractional Helly theorem
  The fractional Helly theorem is a result in combinatorial geometry that generalizes Helly’s theorem by asserting that if a sufficiently large fraction of small subfamilies of convex sets intersect, then a large subfamily of the whole collection has a common intersection.
• D. 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.
• E. Tverberg’s theorem
  Tverberg’s theorem is a fundamental result in combinatorial geometry that guarantees any sufficiently large set of points in Euclidean space can be partitioned into subsets whose convex hulls all intersect.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.