In linear algebra and related areas of mathematics a balanced set, circled set or disk in a vector space is a set S so that for all scalars α with |α| ≤ 1

with

The balanced hull for a set S is the intersection of all balanced sets containing S.

Examples

• in a normed vector space the unit ball is a balanced set

Properties

• the union and intersection of balanced sets is a balanced set
• a set is absolutely convex if and only if it is convex and balanced