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 t1 and t2 collinear with the origin (and
depending on E) such that every point in ⋃{e : e in E} is visible via S from t1 or t2
(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 Krasnosel’skii
number which characterizes arbitrary unions of two or more starshaped sets in
the
