I am fairly new to the use of little-oh notation and have come across many of the nice properties related to the use of this notation online. One that I am struggling to come across is how one may be able to simply expressions with little-oh notation when we are considering compositions. The problem that I am interested in is the following:
Given $o(f(o(n)))$ is there any way in which one might be able to simplify this expression for particular choices of the function $f$. In particular, what could one say about the expression $o(e^{o(n)})$? Can any simplifications to this be made?
I thought one could write $$o(e^{o(n)})=o(1+o(n)+\frac{o(n)^2}{2!}+\cdots)=o(1)+o(n)+\cdots$$ but I am not entirely sure how may one simplify this?