Editing Convex set (section)

=== Star-convex (star-shaped) sets ===
{{main|Star domain}}
Let {{mvar|C}} be a set in a real or complex vector space. {{mvar|C}} is '''star convex (star-shaped)''' if there exists an {{math|''x''<sub>0</sub>}} in {{mvar|C}} such that the line segment from {{math|''x''<sub>0</sub>}} to any point {{mvar|y}} in {{mvar|C}} is contained in {{mvar|C}}. Hence a non-empty convex set is always star-convex but a star-convex set is not always convex.