In
Euclidean space, a
convex set is the
region such that, for every pair of points within the region, every point on the
straight line segment that joins the pair of points is also within the region. For example, a solid
cube is a convex set, but anything that is hollow or has a dent in it, for example, a
crescent shape, is not convex. A
convex curve forms the boundary of a convex set.