Line transversals in families of connected sets in the plane
Line transversals in families of connected sets in the plane
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Shira Zerbib, Iowa State University
In-Person Talk听
We prove that if a family of compact connected sets in the plane听has the property that every three members of it are intersected by a听line, then there are three听lines intersecting all the sets in the family. This answers a听question of Eckhoff from 1993, who proved that under the same condition there are four听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.听Our proofs use the topological KKM theorem.
Joint with Daniel McGinnis.