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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 =

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 =

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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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:
Transcribed Image Text: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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