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Given (Xi,d;), i = 1,n as a metric space and we define the set X = II-1X; =X;*X2*X;*...Xn %3D Show that the maps d' and d": X*X R, are metrics on X, where d' and d" are defined below as follows: d'(x.y)=max;=1 to n di(Xi,Yi) d"(x,y) = E1 d; (X;,Yi) i%3D1

Given (Xi,d;), i = 1,n as a metric space and we define the set X = II-1X; =X;*X2*X;*...Xn %3D Show that the maps d' and d": X*X R, are metrics on X, where d' and d" are defined below as follows: d'(x.y)=max;=1 to n di(Xi,Yi) d"(x,y) = E1 d; (X;,Yi) i%3D1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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on product metric space X we ​​define the following:

d’(x,y)=max from i=1 to n di(xi,yi)

d”(x,y) = sum from 1 to n from di(xi,yi)

Show that d' and d" are metrics on X.

please check the attached picture to see details of the problem.

Given (X¡,d;), i = 1,n as a metric space and we define the set X=[I-1X; = X¡*X,*X;*...X, Show that the maps d'and d": X*X → R, are metrics on X, where d' and d" are defined below as follows: d'(x.y)=max;=1 d¿(x;Yi) to n d"(x,y) = E1 d;(Xi, Yi)
Transcribed Image Text:Given (X¡,d;), i = 1,n as a metric space and we define the set X=[I-1X; = X¡*X,*X;*...X, Show that the maps d'and d": X*X → R, are metrics on X, where d' and d" are defined below as follows: d'(x.y)=max;=1 d¿(x;Yi) to n d"(x,y) = E1 d;(Xi, Yi)
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