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. =)

Results 1 to 3 of 3

- November 1st 2010, 10:18 AM #1

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

- Joined
- Apr 2005
- Posts
- 15,412
- Thanks
- 1328

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 and . Suppose z is contained in both of those sets and apply the triangle inequality to point p, q, and z.

- November 1st 2010, 10:48 AM #3