Hi, I'm having trouble with this problem class question. I literally have no idea where to begin.

Prove that every metric space is a Hausdorff topological space.

Thanks for any help whatsoever. =)

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- Nov 1st 2010, 10:18 AMThroughpointHausdorffness!
Hi, I'm having trouble with this problem class question. I literally have no idea where to begin.

*Prove that every metric space is a Hausdorff topological space.*

Thanks for any help whatsoever. =) - Nov 1st 2010, 10:23 AMHallsofIvy
Shouldn't it be "Hausdorffity"?(Giggle)

Given two points, p and q, let d= d(p,q), the distance between p and q as measured by the metric. Consider the sets $\displaystyle N_{d/3}(p)= \{x| d(p, x)< d/3\}$ and $\displaystyle N_{d/3}(q)= \{y| d(q, y)< d/3\}$. Suppose z is contained in both of those sets and apply the triangle inequality to point p, q, and z. - Nov 1st 2010, 10:48 AMThroughpoint
Nay, my professor repeatedly uses "

*Hausdorffness*" in lectures! =D He's German though.. English isn't his first language..

Anyways, thanks so much! I think I can crack it now.