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: Jordan curve theorem | Statement: [Analysis Situs, subject, Jordan curve theorem]

Target entity: Jordan curve theorem
Context triple: [Analysis Situs, subject, Jordan curve theorem]

• A. Jordan curve theorem chosen
  The Jordan curve theorem is a fundamental result in topology stating that any simple closed curve in the plane divides the plane into exactly two distinct regions, an "inside" and an "outside."
• B. Peano curve
  The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
• C. 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.
• D. Riemann mapping theorem
  The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
• E. Poincaré conjecture
  The Poincaré conjecture is a landmark problem in topology that characterizes the three-dimensional sphere among three-dimensional manifolds and was famously solved by Grigori Perelman in the early 2000s.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.