# Making given metric space bounded

I just encountered a claim, that for any given metric space (X,d), there exists another topologically equivalent metric d' so that (X,d') is bounded. Anyone knowing anything about the proof for this?

## Answers and Replies

morphism
Science Advisor
Homework Helper
Try putting d'=d/(1+d) or min{1,d}.

Ok. I checked the min{1,d} one.