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: [Euler’s polyhedron formula, relatedTo, Jordan curve theorem]

Target entity: Jordan curve theorem
Context triple: [Euler’s polyhedron formula, relatedTo, Jordan curve theorem]

• A. 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.
• B. 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.
• C. 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.
• D. Conway circle theorem
  The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Jordan curve theorem
Triple: [Euler’s polyhedron formula, relatedTo, Jordan curve theorem]

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."

Target entity: Jordan curve theorem
Target entity description: 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."

• A. 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.
• B. 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.
• C. 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.
• D. Conway circle theorem
  The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
• E. 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.
• F. None of above. chosen