Compact convex sets

A compact convex set is a specific type of shape in mathematics that is both "compact" and "convex." "Compact" means the set is closed (includes its boundary points) and bounded (fits within some finite space). "Convex" means that for any two points inside the set, the straight line connecting them also lies entirely within the set. Examples include solid circles or rectangles. These sets are fundamental in mathematics because they have well-behaved properties, making them important in optimization, geometry, and analysis.