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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 ?

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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 $h$.

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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

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