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)?
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)?
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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