A Krasnosel’skiĭ-type theorem for unions of two starshaped sets in the plane
Marilyn Breen · Pacific Journal of Mathematics · 1985
Let S be a simply connected polygonal region in the plane, symmetric with respect to the x and y axes, such that each edge of S is parallel to one of these axes.Assume that for every set E consisting of 6 or fewer edges of S there exist points t λ and t 2 collinear with the origin (and depending on E) such that every point in U{e: e in E) is visible via S from t γ or t 2 (or both).Then S is a union of two starshaped sets.The number 6 is best possible.Furthermore, an example reveals that there is no finite KrasnoseΓskϋ number which characterizes arbitrary unions of two or more starshaped sets in the plane.