Given the discrete metric space < R", o > for n E Nathe discrete metric o defined by the distance functiono(x, y) =0 if x = yif x # yx, y = R¹.1The open ball in the discrete metricspace < R", o > is the singletonB<1 (a) = {a} for each point a ER" if0 < < 1, and the whole spaceB>1(a) = R" for ε > 1.O TrueO FalseRationale:

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Answered: Given the discrete metric space < R", o…

Given the discrete metric space < R", o > for n E Na the discrete metric o defined by the distance function 0 if x = y o(x, y) = x, y ER". 1 if x # y =

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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Question

Given the discrete metric space < R", o > for n E Na
the discrete metric o defined by the distance function
o(x, y) =
0 if x = y
if x # y
x, y = R¹.
1
The open ball in the discrete metric
space < R", o > is the singleton
B<1 (a) = {a} for each point a ER" if
0 < < 1, and the whole space
B>1(a) = R" for ε > 1.
O True
O False
Rationale:

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