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 if and only if:

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

• Results about absorbing sets in vector spaces can be found here.

• Characterization of Convex Absorbing Set in Vector Space

Sources

• Weisstein, Eric W. "Absorbing Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbsorbingSet.html