Local support refers to the concept in convex geometry where a convex set has a supporting hyperplane at a particular point that touches the set without intersecting its interior. This means that, at this point, the hyperplane serves as a boundary, separating the convex set from its outside space while not cutting through the shape. Understanding local support helps in analyzing the properties of convex sets and their geometric interactions with hyperplanes, which are essential for various applications in optimization and analysis.
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