Jordan Curve Theorem

If $J$ is a simple closed curve in $\Bbb{R}^2$, then $\Bbb{R}^2-J$ has two components (an ``inside'' and ``outside''), with $J$ the Boundary of each.

See also Jordan Curve, Schönflies Theorem

References

Rolfsen, D. Knots and Links. Wilmington, DE: Publish or Perish Press, p. 9, 1976.