Hi, I am stuck with the following proofs. In metric space(adsbygoogle = window.adsbygoogle || []).push({});

here, A,B,C are subset of metric space (X,d) and C is bounded

Problem 1.) d(A,B) <=d(A,C)+d(B,C)+diam(C)

Problem 2.)|d(b,A)-d(c,A)| <= d(b,c) where 'b' belongs to 'B' and 'c' belongs to 'C'.

Problem 3)- diam(A U B)<= diam A+ diam B+ d(A,B) ,Here d(A,B)= inf {d(a,b)| a belong to A and b to B}

I think if i get some clue even about one i can handle other one.

Thanks in advance..:)

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# Diameter of Union of two sets

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