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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 {\displaystyle S} {\displaystyle \operatorname {relint} } ] is defined as its interior within the affine hull of S . {\displaystyle S.} In other words,
For any nonempty convex set C ⊆ R n {\displaystyle C\subseteq \mathbb {R} ^{n}} the relative interior can be defined as
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