Definition:Convex Set (Vector Space)

Definition
Let $V$ be a vector space over $\R$ or $\C$.

A subset $A \subseteq V$ is said to be convex :


 * $\forall x, y \in A: \forall t \in \closedint 0 1: t x + \paren {1 - t} y \in A$

Also see

 * Linear Subspace is Convex Set
 * Singleton is Convex Set
 * Intersection of Convex Sets is Convex Set