# Real Analysis: Isometrics

** Please see the attached file for the complete problem description **

Please show all steps involved.

A function f from a metric space (X,d) onto a metric space (Y, (please see the attached file)) is called an isometry if:

(please see the attached file)

a) Show that an isometry is continuous, one-to-one, and its inverse function f^-1 is also continuous .

b) Show that the function f: (0,1] -> [1, infinity) defined by f(x) = 1/x is not an isometry.

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#### Solution Summary

This solution proves a step-by-step explanation of how to perform an analysis of an isometry.

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