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Let $(X,d)$ be a metric space and let $Y$ be a nonempty subset of $X$. Show that $d$ defines a metric space on $Y$.

I'm not sure how to go about this, I was thinking of just checking the properties hold in $Y$, but not sure if that's the correct approach.

Any help is appreciated, thanks.

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You will have to check if the properties hold on $Y$, use that they hold on $X$. –  Stefan Oct 17 '12 at 16:07
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It is the correct approach. Just verify that the required properties of $d$ also hold in $Y$. –  Ayman Hourieh Oct 17 '12 at 16:08
    
Isn't that trivial though? –  Alti Oct 17 '12 at 16:08
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Indeed it is trivial. –  Ayman Hourieh Oct 17 '12 at 16:15
    
Thanks for you help! –  Alti Oct 17 '12 at 16:17

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up vote 2 down vote accepted

This is indeed the correct approach. Just verify that the required properties of $d$ also hold in $Y$. As you have noticed, it is trivial to do so.

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