Definition:Absorbent Set

Definition
Let $\mathcal{X}$ be a vector space over a field $K$ and $W\subseteq \mathcal{X}$. Let $\alpha\in K$ and let us define the set $a\cdot W$ as $a\cdot W:=\left\{ z=a\cdot y,\ y\in W \right\}$. The set $W$ is called absorbent if the following condition holds:


 * $\displaystyle\bigcup_{a\in K}a\cdot W=\mathcal{X}$

which symbolically can be represented as:


 * $K\cdot W = \mathcal{X}$