التحدب الاحداثي و اجتماع اربع مجموعات نجمية في R3

Let A be a set in R3. A is called 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 starshaped set , if and only if ,a point existed in A as (a) ,so that ,every line segment[a,x] for all xÎA lies in A,(it means every point in A was visible via A from a) in this case this set is starshaped with respect to (a) . In this research we will prove the following theorem: If the set A is compact and coordinate convex set in R3 then: The set A is unio‎n of four starshaped sets ,if and only if ,it existed four points in the set A as ,so that , each boundary point of A will be visible via A from one of the points at least