3.1 Let S be the set of all bounded continuous functions f: [a,b] → R. Given two points fand g in X, letd(f,g) = sup{f(x) = g(x) = x= [a, b]}Determine whether d is a metric on S or not.3.2 Define a bounded subset of a metric space (S, d).3.3 Show that a union of any finite number of bounded subsets of a metric space isbounded.

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Answered: 3.1 Let S be the set of all bounded…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3.1 Let S be the set of all bounded continuous functions f: [a, b] → R. Given two points f and g in X, let d(f. g) = sup{f(x) - g(x) : x = [a, b]} Determine whether d is a metric on S or not.