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

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 94E

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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
So if
x = y
o(x, y)
x, y ER¹.
if x = y
The closed ball in the discrete metric
space R", o> is the singleton
Besi (a) = {a} for each point a ER" if
0 < 1, and the whole space
B>1 (a) = R" for ε > 1. Therefore the
closed sets in the discrete metric space
< R", o > are the emptyset Ø, all
singletons {a}, and the whole space R"
O True
O False
Rationale:
Co
=

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