Mazur's Theorem

The generalization of the Schönflies Theorem to $n$-D. 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