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an open ball in the set X, with its radius & satisfying -d(x, a), Vx € X at the open ball Be (x) lies entirely inside the set X. This proves that the set en set.

an open ball in the set X, with its radius & satisfying -d(x, a), Vx € X at the open ball Be (x) lies entirely inside the set X. This proves that the set en set.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 21E
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Given the set X = {x € R³ : d(x, a) <r}, where d is the usual metric on R³. If B₂ (x) is an open ball in the set X, with its radius & satisfying 0 < ε ≤r-d(x, a), Vx X ensures that the open ball B₂(x) lies entirely inside the set X. This proves that the set X is an open set. O True False
Transcribed Image Text:Given the set X = {x € R³ : d(x, a) <r}, where d is the usual metric on R³. If B₂ (x) is an open ball in the set X, with its radius & satisfying 0 < ε ≤r-d(x, a), Vx X ensures that the open ball B₂(x) lies entirely inside the set X. This proves that the set X is an open set. O True False
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