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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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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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.