Prove that a subset D of a metric space M is dense in M iff nonempty for every nonempty open set
so given nonempty we need to show that cl(D)=M, how does this work?
Here is a slightly different discussion of this.
The statement that is a contact point of means that or is a limit point of [i.e. .
So you are asked to show that each point of is a contact point of .
Suppose that but . Then there is a ball that contains no point of .
WHY? And why is that a contradiction?