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.
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