Line transversals in families of connected sets in the plane
Line transversals in families of connected sets in the plane

Shira Zerbib, Iowa State University
Fine Hall 224
InPerson Talk
We prove that if a family of compact connected sets in the plane has the property that every three members of it are intersected by a line, then there are three lines intersecting all the sets in the family. This answers a question of Eckhoff from 1993, who proved that under the same condition there are four lines intersecting all the sets. We also prove a colorful version of this result under weakened conditions on the sets, improving results of Holmsen from 2013. Our proofs use the topological KKM theorem.
Joint with Daniel McGinnis.