Convex set

A convex set is like a playground slide -- it is round and curved rather than straight and pointy. Anything that is inside the slide stays in the slide no matter which way it is facing. The same is true for convex sets. Anything inside a convex set will stay inside the set no matter which direction it is facing. This makes it easier to figure out if a point is part of the set or not.

Related topics others have asked about:

Absorbing set, Bounded set (topological vector space), Brouwer fixed-point theorem, Carathéodory's theorem (convex hull), Choquet theory, Complex convexity, Convex hull, Convex metric space, Convex series, Helly's theorem, Holomorphically convex hull, Integrally-convex set