Closure of Absorbing Set is Absorbing
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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.
$\blacksquare$