Abstract
A subset of projective space is called convex if its intersection with every line is connected. The complement of a projective convex set is again convex. We prove that for any projective convex set there exists a pair of complementary projective subspaces, one contained in the convex set and the other in its complement. This yields their classification up to homotopy.
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Bracho, J., Calvillo, G. Homotopy classification of projective convex sets. Geom Dedicata 37, 303–306 (1991). https://doi.org/10.1007/BF00181406
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DOI: https://doi.org/10.1007/BF00181406