Radial set

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 internal points. 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.

See also

• Absorbing set – Set that can be "inflated" to reach any point
• Algebraic interior – Generalization of topological interior
• Minkowski functional – Function made from a set
• Star domain – Property of point sets in Euclidean spaces