Schoenflies theorem

Target entity: Schoenflies theorem
Context triple: [Jordan curve theorem, relatedTo, Schoenflies 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. 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.
• C. Dehn–Lickorish theorem
  The Dehn–Lickorish theorem is a fundamental result in low-dimensional topology stating that the mapping class group of a closed, orientable surface is generated by finitely many Dehn twists.
• D. 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 \(\mathbb{R}^{2n}\)).
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Schoenflies theorem
Target entity description: The Schoenflies theorem is a result in topology stating that any simple closed curve in the plane bounds a region homeomorphic to a disk, providing a stronger form of the Jordan curve 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. 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.
• C. Dehn–Lickorish theorem
  The Dehn–Lickorish theorem is a fundamental result in low-dimensional topology stating that the mapping class group of a closed, orientable surface is generated by finitely many Dehn twists.
• D. 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 \(\mathbb{R}^{2n}\)).
• E. 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.
• F. None of above. chosen