In mathematics, a subset of a linear space is radial at a given point if for every there exists a real such that for every Geometrically, this means is radial at if for every there is some (non-degenerate) line segment (depend on ) emanating from in the direction of that lies entirely in
Every radial set is a star domain although not conversely.
Relation to the algebraic interior
The points at which a set is radial are called . The set of all points at which is radial is equal to the algebraic interior.
Relation to absorbing sets
Every absorbing subset is radial at the origin and if the vector space is real then the converse also holds. That is, a subset of a real vector space is absorbing if and only if it is radial at the origin. Some authors use the term radial as a synonym for absorbing.