#4 Exercise 4. If d is a metric on the set X, we define dcut : X × X → [0, 1] bydcut (x, y) = min(d(x, y), 1).Show that dcut is a metric that defines the same topology as X.

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Answered: Exercise 4. If d is a metric on the set…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section: Chapter Questions

Problem 17RE

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Exercise 4. If d is a metric on the set X, we define dcut : X × X → [0, 1] by dcut (x, y) = min(d(x, y), 1). Show that dcut is a metric that defines the same topology as X.