Closed curve

A closed curve is a curve the end point of which coincides with the initial point:

$p: [a,b] \rightarrow {\bf R}^n$ and $p(a) = p(b)$.

The closed curve is called simple if this is the only self-intersection.

Jordan theorem. The complement of a simple closed curve in the plane has two connected components.

Closedness is a topological invariant (see also Manifolds).