Jordan Curve Theorem

Topological theorem asserting that every simple closed curve (a continuous injective image of the circle) in the plane separates the plane into exactly two regions: an interior bounded region and an exterior unbounded region, with the curve as their common boundary.

A theorem asserting that every simple closed curve (a continuous embedding of the circle S^1) in the plane separates the plane into exactly two connected components, one bounded (the inside) and one unbounded (the outside), with the curve as their common boundary.