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: topological Helly theorem | Statement: [Helly’s theorem, hasVariant, topological Helly theorem]

Target entity: topological Helly theorem
Context triple: [Helly’s theorem, hasVariant, topological Helly 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. Borsuk’s conjecture in geometry
  Borsuk’s conjecture in geometry is a famous (now disproven in higher dimensions) problem in metric geometry that proposed any bounded set in n-dimensional Euclidean space can be partitioned into n+1 subsets of smaller diameter.
• C. Borsuk–Ulam theorem
  The Borsuk–Ulam theorem is a fundamental result in algebraic topology stating that any continuous map from an n-dimensional sphere to Euclidean n-space maps some pair of antipodal points to the same point.
• D. Tucker’s lemma
  Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
• E. Carathéodory’s theorem in convex geometry
  Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.