Any convex set has the two-piece property. Non-convex sets also can have to two-piece property, as for example the torus of revolution generated by rotating a circle about an axis that does not intersect the circle.

The two-piece property turns out to be equivalent to tightness for surfaces, which gives an important geometric interpretation to tightness.

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

*The Geometry Center*