Quasi-relative interior

In topology, a branch of mathematics, the quasi-relative interior of a subset of a vector space is a refinement of the concept of the interior. Formally, if $$X$$ is a linear space then the quasi-relative interior of $$A \subseteq X$$ is $$\operatorname{qri}(A) := \left\{x \in A : \operatorname{\overline{cone}}(A - x) \text{ is a linear subspace}\right\} $$ where $$\operatorname{\overline{cone}}(\cdot)$$ denotes the closure of the conic hull.

Let $$X$$ is a normed vector space, if $$C \subseteq X$$ is a convex finite-dimensional set then $$\operatorname{qri}(C) = \operatorname{ri}(C)$$ such that $$\operatorname{ri}$$ is the relative interior.