# Math Help - Is it the discreate topology

1. ## Is it the discreate topology

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

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

For $G=\emptyset$, the statement $n\in G$ is always false and it implies everything, in particular $m\in G$ if $m\mid n$. If $n\in \mathbb N$ and $m\mid n$, then $m$ should be an integer.
Hint for the question: if $n=p_1p_2$ where $p_1$ and $p_2$ are prime numbers then a set of the topology which contains n should contain $p_1$ and $p_2$.