Consider the Natural numbers $\displaystyle N$. and $\displaystyle t$ the collection of all subsets $\displaystyle G$ which satisfy the condition: if $\displaystyle {n\in\mathbb{G}}$ and $\displaystyle m|n$, then $\displaystyle {m\in\mathbb{G}}$. Show that $\displaystyle t$ is a topology on $\displaystyle N$. Is it the discrete topology.

I can show all the conditions for $\displaystyle t$ eccept that $\displaystyle {N\in\mathbb}$$\displaystyle t$ and $\displaystyle {(the empty set)\in\mathbb}$$\displaystyle t$

Is it the discrete topology?? I have no idea about this.

help please