That is, given any collection of open sets whose union contains
*A*, only a finite number of the open sets are actually needed to
cover *A*; the rest can be thrown out.

For sets contained in a Euclidean space, such as **R**^3,
a set is compact if, and only if, it is closed (in the sense of
point-set topology) and bounded (i.e., is contained in some
sphere).

For example, a torus or a cube is compact, but a plane in space is not, since it is not bounded.

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

*The Geometry Center*