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..:)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Diameter of Union of two sets

**Physics Forums | Science Articles, Homework Help, Discussion**