Let C be the set 4. Let C₁ be the set of all continuous real-valued functions on I = [0, 1].(a) Show that d: C₁ × C₁ → R defined by d(f, g) ["\ƒ(x) – g(x)] da is a metric on C₁.=(b) Define i : [0, 1] → R by i(x) = x. Give three examples of elements of Ba(i, 1).

According to our guidelines I can answer only Question no. 4(a).

Answered: 4. Let C₁ be the set of all continuous…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 12T

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4. Let C₁ be the set of all continuous real-valued functions on I = [0, 1]. (a) Show that d : C₂ × C'₁ → R defined by d(ƒ, g) = [¹ \ƒ(x) — g(x)| da is a metric on C₁. (b) Define i [0, 1] → R by i(x): = x. Give three examples of elements of Ba(i, 1).