Schönflies Theorem
If 
is a simple closed curve in 
, the closure of one of the components of 
is Homeomorphicwith the unit 2-Ball. This theorem may be proved using the Riemann Mapping Theorem, but the easiest proof isvia Morse Theory.
The generalization to 
-D is called Mazur's Theorem. It follows from the Schönflies theorem that any twoKnots of 
in 
or are equivalent.
References
Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 9, 1976. Thomassen, C. ``The Jordan-Schönflies Theorem and the Classification of Surfaces.'' Amer. Math. Monthly 99, 116-130, 1992.
- Doubly Magic Square
- Dougall-Ramanujan Identity
- Dougall's Theorem
- Doughnut
- Douglas-Neumann Theorem
- Dovetailing Problem
- Dowker Notation
- Down Arrow Notation
- Dozen
- Dragon Curve
- Dragon Fractal
- Draughts
- Drinfeld's Symmetric Space
- Droz-Farny Circles
- Drum
- D-Statistic
- D-Triangle
- Dual Basis
- Dual Bivector
- Dual Graph
- Duality Principle
- Duality Theorem
- Dual Map
- Dual Polyhedron
- Dual Scalar