Closure of Absorbing Set is Absorbing

Theorem

Let $\GF \in \set {\R, \C}$.

Let $X$ be a vector space over $\GF$.

Let $A \subseteq X$ be an absorbing set.

Then $A^-$ is absorbing.

Proof

From the definition of closure, we have $A \subseteq A^-$.

From Superset of Absorbing Set is Absorbing, $A^-$ is absorbing.

$\blacksquare$