Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Can anyone explain to me what is the idea of relative interior of a convex hull of a set of finite points ? For interior of a set , I understand that it is a set which excludes its boundary. Is interior of a set a subset of relative interior of a set ?

share|improve this question

1 Answer 1

The relative interior refers to the fact, that you only consider the interior of set w.r.t. its affine hull.

Here is one example. Take a 3d point set, all points lie on a common plane $h$. The convex hull of this set is a "2d object" with affine hull is $h$. Its interior in $\mathbf{R}^3$ is $\emptyset$. The relative interior however is the convex hull without vertices and edges. In other words it is the interior w.r.t. the plane $h$.

share|improve this answer
    
So let's say I have two points and I take their affine hull. The relative interior of this two points is the set which contains the points on the affine hull of the two points, which is an edge ? Am I right ? –  hong wai Dec 10 '12 at 12:26
    
Do you mean you take the convex hull of the two points and consider then the relative interior? Otherwise it doesn't make sense. The relative interior of a finite union of singeltons will be empty. –  A.Schulz Dec 10 '12 at 13:03

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.