Hyperplane transversal to coloured sets

Edgardo Roldan Pensado

Abstract

Hadwiger's transversal theorem gives conditions for a family of convex sets in the plane to have a line transversal. A higher dimensional version was obtained by Goodman, Pollack and Wenger, and recently a colourful version appeared due to Arocha, Bracho and Montejano. We show that it is possible to combine both results to obtain a coloured version of Hadwiger's theorem in higher dimensions.