4. Let E CRd, and for each nE N, define On as the set On z d(x, E) 1/n) Recall that d(x, E) inf{| - el : e E E}. Prove that for each n e N, On is open

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.5: Inequalities In A Triangles
Problem 35E: Prove by the indirect method: Given: MPN is not isosceles Prove: PMPN
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Related questions
Question
4. Let E CRd, and for each nE N, define On
as the set
On z d(x, E) 1/n)
Recall that d(x, E)
inf{| - el : e E E}. Prove that for each n e N, On is open
Transcribed Image Text:4. Let E CRd, and for each nE N, define On as the set On z d(x, E) 1/n) Recall that d(x, E) inf{| - el : e E E}. Prove that for each n e N, On is open
Expert Solution
Step 1

To prove the openness of the given sequence of sets

Step 2

Problem statement

EcRDefine
O {x:d(x, E)<,neN
п
where,d(x, E) inf x-e|;ee E
To show O is open.
steps

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