Definition:Absorbing Set

Definition

Let $\Bbb F$ 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:

$\ds X = \bigcup_{n \mathop = 1}^\infty n A$

where $n A$ is the dilation of $A$ by $n$.

Also see

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

Sources

• 2011: Graham R. Allan and H. Garth Dales: Introduction to Banach Spaces and Algebras ... (previous) ... (next): $2.1$: Normed Spaces