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 AM #1

- Nov 1st 2010, 10:23 AM #2

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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 $\displaystyle N_{d/3}(p)= \{x| d(p, x)< d/3\}$ 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 AM #3