Share
Explore BrainMass

Real analysis metric spaces

(See attached file for full problem description)

7. If d is a real-valued function on which for all x, y, and z in X satistifes
d(x,y) = 0 if and only if x=y
d(x,y)+d(x,z)≥d(y,z)
show that d is a metric on X.

Attachments

Solution Preview

Proof:
(1) d(x,y)>=0
Since d(x,y)+d(x,z)>=d(y,z), especially, we select z=y and from the condition, we know d(z,z)=0, then we have d(x,y)+d(x,y)>=d(z,z)=0, ...

Solution Summary

This solution is comprised of a detailed explanation to show that d is a metric on X.

$2.19