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0 if x = y o(x, y) 1 if x #y x, y ER". The open ball in the discrete metric space R", o> is the singleton Be<1(a) = {a} for each point a € R" if 0 < & ≤ 1, and the whole space Be>1(a) = R" for ε > 1. O True False Reset Selection Rationale:

0 if x = y o(x, y) 1 if x #y x, y ER". The open ball in the discrete metric space R", o> is the singleton Be<1(a) = {a} for each point a € R" if 0 < & ≤ 1, and the whole space Be>1(a) = R" for ε > 1. O True False Reset Selection Rationale:

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 € N and the discrete metric o defined by the distance function o(x, y) = 0 if x=y 1 if xy x, y ≤R". The open ball in the discrete metric space < R", o > is the singleton B₂<1(a) = {a} for each point a ER" if 0 < & ≤ 1, and the whole space Be>1(a) = R″ for ɛ > 1. True False Reset Selection Rationale:
Transcribed Image Text:Given the discrete metric space R", o for n € N and the discrete metric o defined by the distance function o(x, y) = 0 if x=y 1 if xy x, y ≤R". The open ball in the discrete metric space < R", o > is the singleton B₂<1(a) = {a} for each point a ER" if 0 < & ≤ 1, and the whole space Be>1(a) = R″ for ɛ > 1. True False Reset Selection Rationale:
Given the discrete metric space R", o for n € N and the discrete metric o defined by the distance function o(x, y) = 0 if x = y if xy x, y ER". 1 The closed ball in the discrete metric space < R", o > is the singleton B<1(a) = {a} for each point a ER" if 0 < ɛ ≤ 1, and the whole space Bɛ>1 (a) = R" for ɛ > 1. Therefore the closed sets in the discrete metric space R", o are the emptyset Ø, all singletons {a}, and the whole space R". True False
Transcribed Image Text:Given the discrete metric space R", o for n € N and the discrete metric o defined by the distance function o(x, y) = 0 if x = y if xy x, y ER". 1 The closed ball in the discrete metric space < R", o > is the singleton B<1(a) = {a} for each point a ER" if 0 < ɛ ≤ 1, and the whole space Bɛ>1 (a) = R" for ɛ > 1. Therefore the closed sets in the discrete metric space R", o are the emptyset Ø, all singletons {a}, and the whole space R". True False
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