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In mathematics, given a linear space X, a set $$A \subseteq X$$ is radial at the point $$x_0 \in A$$ if for every $$x \in X$$ there exists a t_x > 0 such that for every $$t \in [0,t_x], x_0 + tx \in A$$. In set notation, A is radial at the point $$x_0 \in A$$ if

$$\bigcup_{x \in X}\ \bigcap_{t_x > 0}\ \bigcup_{t \in [0,t_x]} \{x_0 + tx\} \subseteq A. The set of all points at which \( A \subseteq 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 $$A \subseteq X$$ 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.

References

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