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 
dimensions is called Mazur's
theorem. It follows from the Schönflies theorem that any two knots
of 
in 
or 
are equivalent.
