 Convex set

A convex set contains every line segment joining two of its points.

In mathematics, particularly in the field of convex analysis, a **convex set** is defined as a subset \( C \) of a vector space such that, for any two points \( x \) and \( y \) in \( C \), the line segment connecting \( x \) and \( y \) is also entirely contained within \( C \).