# Connected:

A surface is *connected* if, given any two points on the surface,
there is a path (that stays on the surface) that connects the two
points. Essentially, a surface is connected if it is in one piece,
and not connected if it is in more than one piece. The pieces of a
disconnected surface are called the *connected components* of the
surface.
For example, a sphere and the
torus
are connected surfaces: you can get from any point to any other point
by staying on the surface. On the other hand, a pair of sphere is
disconnected, since you can not get from one sphere to the other while
staying on the surface of the two spheres.

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

*The Geometry Center*