Another Abstraction of the Erdős-Szekeres Happy End Theorem

Abstract

The Happy End Theorem of Erdős and Szekeres asserts that for every integer $n$ greater than two there is an integer $N$ such that every set of $N$ points in general position in the plane includes the $n$ vertices of a convex $n$-gon. We generalize this theorem in the framework of certain simple structures, which we call "happy end spaces".