I have to prove the following:
Let $F \subseteq \mathbb{R}^\mathbb{N}.$
Define:
$ { \mathcal{O} (F) = \{ g : \mathbb{N}}\rightarrow > \mathbb{R}| \exists f \in F\exists C>0\exists n_0 \in\mathbb{N}\forall > n \in \mathbb{N}(n \geq n_0 \rightarrow |g(n)| \le C|f(n)| \}$Prove if $\mathcal{O} : {2^\mathbb{R}}^\mathbb{N} \rightarrow {2^\mathbb{R}}^\mathbb{N} $ is a hull operator. What is his Universe $U$?
I don't know what to show exactly. Any help would be appreciated.
Thanks.