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