For example, if a circle is mapped into the plane as a figure-8, then the crossing is a double point. If a surface is mapped into space so that there is self-intersection, the points of self-intersection are formed by double-points.

Generically, the double-points of a surface in space form curves. For
an immersion, they will form
closed
curves. These curves are called the *double curves* or the
*double locus* of the mapping, and the *double set* is the
set of points of the surface that map to the double locus.

* 8/12/94 dpvc@geom.umn.edu -- *

*The Geometry Center*