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 is a linear space then the quasi-relative interior of is where denotes the closure of the conic hull.[1]
Let is a normed vector space, if is a convex finite-dimensional set then such that is the relative interior.[2]
See also
edit- Interior (topology) – Largest open subset of some given set
- Relative interior – Generalization of topological interior
- Algebraic interior – Generalization of topological interior
References
edit- ^ Zălinescu 2002, pp. 2–3.
- ^ Borwein, J.M.; Lewis, A.S. (1992). "Partially finite convex programming, Part I: Quasi relative interiors and duality theory" (pdf). Mathematical Programming. 57: 15–48. doi:10.1007/bf01581072. Retrieved October 19, 2011.
- Zălinescu, Constantin (30 July 2002). Convex Analysis in General Vector Spaces. River Edge, N.J. London: World Scientific Publishing. ISBN 978-981-4488-15-0. MR 1921556. OCLC 285163112 – via Internet Archive.