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

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \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 $C \subset X$ is a convex finite-dimensional set then $\operatorname{qri}(C) = \operatorname{ri}(C)$ such that $\operatorname{ri}$ is the relative interior.

See also

• Interior (topology)
• Relative interior
• Algebraic interior