Q2 From Q1, we know that du(f.g) = sup{f(r) - g(x): I} defines a metric...
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Q2 From Q1, we know that du(f.g) = sup{f(r) - g(x): € I} defines a metric on C(I) where I = [0, 1]. [12 marks] (a) Does this still define a metric if the interval I is changed to 7 = (0, 1)? Explain your answer. (b) Does this still define a metric if I = R? Explain your answer. (e) What if, instead of continuous functions on I = [0, 1], we considered the set of all bounded functions on I? Briefly explain your answer. Q2 From Q1, we know that du(f.g) = sup{f(r) - g(x): € I} defines a metric on C(I) where I = [0, 1]. [12 marks] (a) Does this still define a metric if the interval I is changed to 7 = (0, 1)? Explain your answer. (b) Does this still define a metric if I = R? Explain your answer. (e) What if, instead of continuous functions on I = [0, 1], we considered the set of all bounded functions on I? Briefly explain your answer.
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Related Book For
The Legal Environment of Business A Critical Thinking Approach
ISBN: 978-0134074030
8th edition
Authors: Nancy K. Kubasek, Bartley A. Brennan, M. Neil Browne
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