Clear visibility and unions of two starshaped sets in the plane
Marilyn Breen · Pacific Journal of Mathematics · 1984
Let S be a compact set in R 2 .Assume that for every finite set F in bdry S there exist points s and t (depending on F) such that every point of F is clearly visible via S from at least one of s or /.Then S is a union of two starshaped sets.If "clearly visible" is replaced by the weaker term "visible", then the result fails.