I am considering $(X,d)$, which is a set with a discrete metric and $D \subset X$. With these conditions given, I am supposed to show that $\partial D = \emptyset $. Further I am supposed to describe all open (closed) sets in $(X,d)$.
I kinda have the idea of why $\partial D = \emptyset$. I think it has to do with the fact that the metric space is endowed with a discrete metric. But i certainly don't know where to start. This is also making the second part a bit difficult.
I'd be really happy if someone could help me.