An extension of the Erdős-Szekeres theorem on large angles

The existence of a functionn(ε) (ε>0) is established such that given a finite setV in the plane there exists a subsetW⊆V, |W|<n(ε) with the property that for anyv εV\W there are two pointsw1,w2 εW such that the angle ∢(w1vw2)>π-ε.