The Cartesian product X = X1 x X2 of two metric spaces (X1, d1) and (X2, d2) can be made into metric space (X, d) in many ways. For instance, show that a metric d is defined by d(x, y) = d,(x1, y1) + d2(x2, y2), Where x = (x,x2), y = (y1,Y2). Question # 02 Show that another metric on X in question 01 is defined by d(x,y) = Jd,(x1, y,)² + d¿(x2, Y2)². Question # 03 Show that another metric on X in question 01 is defined by d(x,y) = max[d,(x1,Y1), dz(x2, Y2)]- Question # 04 Define new metric which is different from giving in above questions on X in question 01.

The Cartesian product X = X1 x X2 of two metric spaces (X1, d1) and (X2, d2) can be made into metric space (X, d) in many ways. For instance, show that a metric d is defined by d(x, y) = d,(x1, y1) + d2(x2, y2), Where x = (x,x2), y = (y1,Y2). Question # 02 Show that another metric on X in question 01 is defined by d(x,y) = Jd,(x1, y,)² + d¿(x2, Y2)². Question # 03 Show that another metric on X in question 01 is defined by d(x,y) = max[d,(x1,Y1), dz(x2, Y2)]- Question # 04 Define new metric which is different from giving in above questions on X in question 01.

Name: Please solve Question 4. Question # 01The Cartesian product X = X1 × X
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Description: Please solve Question 4. Question # 01The Cartesian product X = X1 × X2 of two metric spaces (X,, d,) and (X2, d2) can be made intometric space (X, d) in many ways. For instance, show that a metric d is defined byd(x, y) = d,(x1, y,) + d2(x2, y2),Whe

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.3: Vectors

Problem 60E

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