In mathematics, given a linear space X , a set A ⊆ X is radial at the point x 0 ∈ A if for every x ∈ X there exists a t x > 0 such that for every t ∈ [ 0 , t x ] , x 0 + t x ∈ A . Geometrically, this means A is radial at x 0 if for every x ∈ X a line segment emanating from x 0 in the direction of x lies in A , where the length of the line segment is required to be non-zero but can depend on x .
The set of all points at which A ⊆ X 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 A ⊆ X 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.
