Given a function f : D → R defined on a set D, recall that the modulus ofcontinuity is a functionw(x0, 8) = sup{|f (x) – f(xo)| : x E D, \x – xo] < 8}.Assume that f is uniform continuous on D. Prove that the function h(8)suproED W(x0, 8) satisfies:lim h(8) = 0.8→0+

The key Idea is that as f is uniformly continuous, we can interchange the limitδ & supx₀ Then…

Answered: Given a function f : D → R defined on a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...

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Given a function f : D → R defined on a set D, recall that the modulus of continuity is a function w(x0, 8) = sup{\f (x) – f(x0)| : x E D, x – xo| < 8}. Assume that f is uniform continuous on D. Prove that the function h(8) suproED W(x0, 8) satisfies: lim h(8) = 0. 8→0+