Abstract
A set of points is a cup, if it lies on the graph of convex function. Similarly a set of points is a cap, if it lies on concave function.
A cup/cap is open, if there is no point above the cup/cap. There is a Ramsey-type theorem, which says that if N is sufficiently large, we always find either open cup of size k or open cap of size l.
We present a simple proof for open cups and open caps. Moreover we improve the bounds on N.