Quasi-relative interior
# 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.

