In mathematics, given a linear space , a set is radial at the point if for every there exists a such that for every , . Geometrically, this means is radial at if for every a line segment emanating from in the direction of lies in , where the length of the line segment is required to be non-zero but can depend on .
The set of all points at which is radial is equal to the algebraic interior. The points at which a set is radial are often referred to as internal points.
A set is absorbing if and only if it is radial at 0. Some authors use the term radial as a synonym for absorbing, i. e. they call a set radial if it is radial at 0.
- Jaschke, Stefan; Küchler, Uwe (2000). "Coherent Risk Measures, Valuation Bounds, and ()-Portfolio Optimization".
- Nikolaĭ Kapitonovich Nikolʹskiĭ (1992). Functional analysis I: linear functional analysis. Springer. ISBN 978-3-540-50584-6.
- Aliprantis, C.D.; Border, K.C. (2007). Infinite Dimensional Analysis: A Hitchhiker's Guide (3 ed.). Springer. pp. 199–200. doi:10.1007/3-540-29587-9. ISBN 978-3-540-32696-0.
- John Cook (May 21, 1988). "Separation of Convex Sets in Linear Topological Spaces" (pdf). Retrieved November 14, 2012.
- Schaefer, Helmuth H. (1971). Topological vector spaces. GTM. 3. New York: Springer-Verlag. ISBN 0-387-98726-6.