A FINITE FAMILY OF PSEUDODISCS MUST INCLUDE A 'SMALL' PSEUDODISC

摘要

We show that there is an absolute constant c ≤156 such that in every finite family F of pseudodiscs in the plane one can find a member D ∈ F such that among all of the pseudodiscs in F intersecting D there are at most c pairwise disjoint sets.