 Jordan curve theorem

Every simple closed curve on the sphere separates it into two connected components, each having the curve as its boundary.

A topological surface is a Hausdorff second-countable space locally homeomorphic to the plane.

The Jordan Curve Theorem is a fundamental result in topology, a branch of mathematics that studies properties of spaces that are preserved under continuous deformations. The theorem states that any simple closed curve in a plane (a curve that does not intersect itself and forms a complete loop) divides the plane into two distinct regions: an "inside" and an "outside.