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Answer to Question #72876 in Functional Analysis for Sajid
Question #72876
Let D be a metric on X determined all constant k s.t
(k+d) is a metric. Give its Hint or prove it shortly.
(k+d) is a metric. Give its Hint or prove it shortly.
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Comments
One should verify conditions for (k+d) to be a metric given the function d is a metric. The solution explains the reasons why there should be k=0 in this case. By definition,,if d is a metric then d(x,y)>=0,d(x,y)=0 if and only if x=y, d(x,y)=d(y,x), d(x,z)
Can you please explain briefly I can't understand.and tell about kb is a metric space on X?
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