Relative interior
In mathematics, the relative interior of a set is a refinement of the concept of the interior, which is often more useful when dealing with low-dimensional sets placed in higher-dimensional spaces.
Formally, the relative interior of a set S is defined as its interior within the affine hull of S. In other words,
where is the affine hull of S, and is a ball of radius centered on. Any metric can be used for the construction of the ball; all metrics define the same set as the relative interior.
For any nonempty convex set the relative interior can be defined as
