التحدب الإحداثي واجتماع أربع مجموعات نجمية في R2

In the Euclidean plane, we say that the set is coordinate convex set, if and only if, any parallel line to any coordinate axes was intersected with is convex set . an‎d we say that the set is star shaped set, if and only if, a point existed in A as (a), so that, every line segment [a, x] for all lie in A , in this case we say that every point was visible via A from a . In this study will prove the following theory: “If the set A is coordinate convex and compact set in the Euclidean plane then: The set A is unio‎n of four star shaped sets, if and only if, it existed in the set A four points as a,b,c,d , so that, every boundary point of A in this set will be visible from a,b,c or d at least.”