somebody to help me, consider $\mathbb{Z}$ and $\mathbb{Q}$ as subspaces of $\mathbb{R}$ with the usual topology. The question is to show that every point of $\mathbb{Z}$ is isolated,and to show that no point of $\mathbb{Q}$ is isolated.
The definition for isolated point ; a point $x \in X$ is said to be isolated point of if the one -point set $\{x\}$ is open in $X$
THANKS!