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–Brouwer separation theorem | Statement: [Jordan curve theorem, generalizedBy, Jordan–Brouwer separation theorem]

Target entity: Jordan–Brouwer separation theorem
Context triple: [Jordan curve theorem, generalizedBy, Jordan–Brouwer separation theorem]

• A. 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."
• B. 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.
• 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. Smale’s paradox
  Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
• E. Whitney embedding theorem
  The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
• 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–Brouwer separation theorem
Triple: [Jordan curve theorem, generalizedBy, Jordan–Brouwer separation theorem]

The Jordan–Brouwer separation theorem is a fundamental result in topology stating that any (n−1)-dimensional sphere embedded in n-dimensional Euclidean space divides the space into exactly two disconnected regions with the sphere as their common boundary.

Target entity: Jordan–Brouwer separation theorem
Target entity description: The Jordan–Brouwer separation theorem is a fundamental result in topology stating that any (n−1)-dimensional sphere embedded in n-dimensional Euclidean space divides the space into exactly two disconnected regions with the sphere as their common boundary.

• 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. 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.
• 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. Smale’s paradox
  Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
• E. Whitney embedding theorem
  The Whitney embedding theorem is a fundamental result in differential topology stating that any smooth n-dimensional manifold can be embedded as a submanifold of Euclidean space of sufficiently high dimension (specifically \(\mathbb{R}^{2n}\)).
• F. None of above.