If is a simple closed curve in , the closure of one of the components of is Homeomorphic with the unit 2-Ball. This theorem may be proved using the Riemann Mapping Theorem, but the easiest proof is via Morse Theory.

The generalization to -D is called Mazur's Theorem. It follows from the Schönflies theorem that any two Knots 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.

© 1996-9

1999-05-26