Mazur's Theorem
The generalization of the Schönflies theorem to n dimensions. A smoothly embedded n-hypersphere in an (n+1)-hypersphere separates the (n+1)-hypersphere into two components, each homeomorphic to (n+1)-balls. It can be proved using Morse theory.
See also
Ball, Hypersphere, Morse TheoryExplore with Wolfram|Alpha
WolframAlpha
Cite this as:
Weisstein, Eric W. "Mazur's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MazursTheorem.html