Definition:Absorbent Set

Definition
Let $V$ be a vector space over a field $K$.

Let $W \subseteq V$ be a subset of $V$.

Let $a \in K$.

Let the set $a \cdot W$ be defined as:


 * $a \cdot W := \left\{{a \cdot y: y \in W} \right\}$

Then $W$ is an absorbent set iff:


 * $\displaystyle \bigcup_{a \mathop \in K} a \cdot W = V$

which symbolically can be represented as:


 * $K \cdot W = V$