Answered: Let F be a nonempty set of functions…

Let F be a nonempty set of functions that map [0,1] into [0,1]. For 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 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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