nLab absorbing subset

Definition

Let $V$ be a vector space over $\mathbb{R}$ or $\mathbb{C}$. A subset $B$ of $V$ is said to be absorbing if $\bigcup_{r \gt 0} r B = V$.

Examples

• The unit ball in a seminormed vector space is absorbing.
• The linear span of absolutely convex set $C$ in a vector space has $C$ as an absorbing set.

Related concepts

• convex set
• balanced set
• absolutely convex set

category: functional analysis