Let $${\displaystyle X}$$ be a vector space over the field $${\displaystyle \mathbb {K} }$$ of real or complex numbers.
Notation
If $${\displaystyle S}$$ is a set, $${\displaystyle a}$$ See more

• Absolutely convex set – convex and balanced set
• Absorbing set – Set that can be "inflated" to reach any point See more

The empty set is a balanced set. As is any vector subspace of any (real or complex) vector space. In particular, $${\displaystyle \{0\}}$$ is always a balanced set.
Any non-empty set … See more

Properties of balanced sets
A balanced set is not empty if and only if it contains the origin. By definition, a set is absolutely convex if … See more