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: Brouwer invariance of domain | Statement: [Jordan curve theorem, relatedTo, Brouwer invariance of domain]

Target entity: Brouwer invariance of domain
Context triple: [Jordan curve theorem, relatedTo, Brouwer invariance of domain]

• A. Brouwer fixed-point theorem chosen
  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.
• B. Thom transversality theorem
  The Thom transversality theorem is a fundamental result in differential topology that guarantees generic smooth maps are transverse to given submanifolds, underpinning the study of stable phenomena and cobordism.
• C. Tychonoff theorem for products of compact spaces
  The Tychonoff theorem for products of compact spaces is a fundamental result in topology stating that any product of compact topological spaces is compact, a statement that is equivalent in strength to the axiom of choice.
• D. Alexandrov–Hausdorff theorem
  The Alexandrov–Hausdorff theorem is a result in descriptive set theory that characterizes analytic sets as continuous images of Baire space, playing a key role in the study of definable sets in Polish spaces.
• E. Sard's theorem
  Sard's theorem is a fundamental result in differential topology stating that the set of critical values of a smooth map between manifolds has measure zero, implying that almost all values are regular.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.