Exercise 4 Exercise 4. Suppose (Y, d) is a complete metric space. Consider XC Y as a metric space(X,d) with the induced metric from the metric d on Y.If (X,d) is a completion of X, show that there is an isometry I : X → Y which is theidentity on X. What is the image I(X)?

Answered: Image /qna-images/answer/2aa95a8b-ce3d-4e6e-aa84-d76cd94c6a71.jpg

Answered: Exercise 4. Suppose (Y,d) is a complete…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 10E

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Exercise 4. Suppose (Y,d) is a complete metric space. Consider XC Y as a metric space (X,d) with the induced metric from the metric d on Y. If (X,d) is a completion of X, show that there is an isometry I : X → Y which is the identity on X. What is the image I(X)?