Radial Set



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What is Radial set?

In mathematics, given a linear space X, a set A ⊆ X is radial at the point if for every x ∈ X there exists a such that for every , . Geometrically, this means A is radial at if for every x ∈ X a line segment emanating from in the direction of x lies in , 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.

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مجموعة شعاعية (ar)径向集 (zh)

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