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Let F be a nonempty set of functions that map [0, 1] into [0, 1] . For all f and g in F, define d(f, g) = sup{|f(x)-g(x)|: x in [0,1]}. Show that d is a metric on f.

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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Let F be a nonempty set of functions that map [0, 1] into [0, 1] . For all f and g in F, define d(f, g) = sup{|f(x)-g(x)|: x in [0,1]}. Show that d is a metric on f.

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