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. =)
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.