Definition:Absorbing Set

Definition
Let $\GF$ be a subfield of $\C$.

Let $X$ be a vector space over $\Bbb F$.

Let $A \subseteq X$.

We say that $A$ is absorbing :
 * for all $x \in X$ there exists $t \in \R_{> 0}$ such that $x \in \alpha C$ for $\cmod \alpha \ge t$

where $t A$ denotes the dilation of $A$ by $t$.

Also see

 * Characterization of Convex Absorbing Set in Vector Space