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We study intersections of projective convex sets in the sense of Steinitz. Ina projective space, an intersection of a nonempty family of convex sets splitsinto multiple connected components each of which is a convex set. Hence, suchan intersection is called a multi-convex set. We derive a duality for saturatedmulti-convex sets: there exists an order anti-isomorphism between nonemptysaturated multi-convex sets in a real projective space and those in the dualprojective space. In discrete geometry and computational geometry, theseresults allow to transform a given problem into a dual problem which sometimesis easier to solve. This will be pursued in a later paper.

Multi-convex sets in real projective spaces and their duality