Let a subset of . We say that is convex when, for any pair of points in , the segment lies entirely inside .
The former statement is equivalent to saying that for any pair of vectors in , the vector is in for all .
If is a convex set, for any in , and any positive numbers such that the vector
is in .
More generally, the same definition works for any vector space over an ordered field.
A polyconvex set is a finite union of compact, convex sets.
Remark. The notion of convexity can be generalized to an arbitrary partially ordered set: given a poset (with partial ordering ), a subset of is said to be convex if for any , if is between and , that is, , then .
|Date of creation||2013-03-22 11:46:35|
|Last modified on||2013-03-22 11:46:35|
|Last modified by||drini (3)|