Let m EN, m > 2 be a fixed, and consider the set Rn with a metric function d,m defined by the formula 1 m dm(x, y) = dm((x1, x2, ..., Xxn), (Y1, Y2,.., yn) = Ix;- yilm for each x = (x1, X2, ... , Xn), y = (y1, Y2, .., Yn) E R". i=D1 %3D The pair (IR", dm) is a metric space. (check ?)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let m E N, m > 2 be a fixed, and consider the set R" with a metric function d,m
defined by the formula
1
п
m
dm(x, y) = dm((x1, x2, ... , xn), (yı, Y2, .. , Yn)) =
> lx;- Yilm
for each x =
(x1, X2, ..., Xn), y = (y1, Y2, ..., Yn) E R".
%=D1
%3D
The pair (R", dm) is a metric space. (check ?)
Transcribed Image Text:Let m E N, m > 2 be a fixed, and consider the set R" with a metric function d,m defined by the formula 1 п m dm(x, y) = dm((x1, x2, ... , xn), (yı, Y2, .. , Yn)) = > lx;- Yilm for each x = (x1, X2, ..., Xn), y = (y1, Y2, ..., Yn) E R". %=D1 %3D The pair (R", dm) is a metric space. (check ?)
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