# Thread: Hausdorffness!

1. ## Hausdorffness!

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. =)

2. Shouldn't it be "Hausdorffity"?

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 $N_{d/3}(p)= \{x| d(p, x)< d/3\}$ and $N_{d/3}(q)= \{y| d(q, y)< d/3\}$. Suppose z is contained in both of those sets and apply the triangle inequality to point p, q, and z.

3. 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.