This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Closed curve

### From Mathematics Is A Science

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

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).