I am trying to understand the first example of Big-Oh notation in Computational Complexity:A Modern Approach page 9.
If $f(n) = 100nlogn$ and $g(n) = n^2$ then we have the relations $f = O(g)$, $g = Ω(f)$, $f = o(g)$, $g = ω(f)$.
I understood why $f = O(g)$ and $f = o(g)$ . As for the rest I didn't. For instance in order for $g$ to be equal to $Ω(f)$ we must have $g = O(f)$.
How can we prove that $g = O(f)$ and $g=o(f)$?