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: Kakutani fixed-point theorem | Statement: [Shizuo Kakutani, hasTheoremNamedAfter, Kakutani fixed-point theorem]

Target entity: Kakutani fixed-point theorem
Context triple: [Shizuo Kakutani, hasTheoremNamedAfter, Kakutani fixed-point theorem]

• A. Kakutani fixed-point theorem chosen
  The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
• B. Glicksberg fixed-point theorem
  The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
• C. Schauder fixed-point theorem
  The Schauder fixed-point theorem is a fundamental result in functional analysis that guarantees the existence of fixed points for continuous compact mappings on convex closed subsets of Banach spaces, generalizing the Brouwer fixed-point theorem to infinite-dimensional settings.
• D. Brouwer fixed-point theorem
  The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
• E. Banach fixed-point theorem
  The Banach fixed-point theorem is a fundamental result in metric space theory that guarantees the existence and uniqueness of a fixed point for any contraction mapping and provides a method for finding it via iterative approximation.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target predicate: hasTheoremNamedAfter
Context triple: [Shizuo Kakutani, hasTheoremNamedAfter, Kakutani fixed-point theorem]

• A. hasAwardNamedAfter
  Indicates that an entity has an award that is named in honor of another entity.
• B. hasLawNamedAfter
  Indicates that a law or piece of legislation is named in honor of, or directly after, a particular entity.
• C. hasAsteroidNamedAfter
  Indicates that an asteroid has been officially named in honor of a particular entity.
• D. hasHeritageSiteNamedAfter
  Indicates that one entity has a heritage site that is named after another entity.
• E. hasCraterNamedAfter
  Indicates that a crater is named in honor of a particular person, place, or entity.
• F. None of above. chosen