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## Main Question or Discussion Point

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?

- Thread starter jostpuur
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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?

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morphism

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Try putting d'=d/(1+d) or min{1,d}.

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

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