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?

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- Nov 25th 2011, 05:50 PMwopashuiprove that D is dense
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? - Nov 25th 2011, 07:54 PMDrexel28Re: prove that D is dense
- Nov 26th 2011, 07:02 AMPlatoRe: prove that D is dense
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?