We prove duals of Radon's theorem, Helly's theorem, Carathéodory's theorem, and Kirchberger's theorem for arrangements of pseudolines in the real projective plane, which generalize the original versions of those theorems for plane configurations of points. We also prove a topological generalization of the pseudoline-dual of Helly's theorem. © 1982.
Goodman, J. E., & Pollack, R. (1982). Helly-type theorems for pseudoline arrangements in P2. Journal of Combinatorial Theory, Series A, 32(1), 1–19. https://doi.org/10.1016/0097-3165(82)90061-9