العلاقة بين المجموعات المحدبة إحداثياً والمجموعات النجمية في R3

Let A be a set in R3. A is said to be a coordinate convex set if and only if any parallel line to any coordinate axes oX , oY , oZ was intersected with A is convex set A is called a star-shaped set, if and only if ,there exists a points in A as (a) ,such that ,every line segment[a, x] for all xÎA lies in A, in this case this set is star-shaped with respect to (a) ,and every point in A was visible via A from a. In this paper we will prove a set of theorems, some of which are: 1) -If the set A is coordinate convex in the Euclidean space (R3) then: The set A is unio‎n of six star-shaped sets, if and only if, there exists a point in the set A six points as a, b, c, d, e, f , so that , each point in A would be visible via A from a, b , c, d, e, f at least . 2)-Each convex set is coordinate convex set, but the opposite in general is not true 3) –It is not necessary for each coordinate convex to be a star-shaped set.