Exercise 6.41. Let E be a nonempty set in Rn. Then the distance of a point x E Rto E is defined bydist (x, E) = inf {||x - y|| : y = E}.Prove the following:(i) x E E if and only if dist (x, E) = 0.(ii) E is closed if and only if dist (x, E) > 0 for all x € EC.(iii) For each x ER", there exists a point y in E such that dist (x, E) = |x-y||.

Answered: Image /qna-images/answer/3bbf7775-25e2-42ff-aff4-bea497973d25.jpg

Answered: Exercise 6.41. Let E be a nonempty set…

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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