Exercise 6.40 please Exercise 6.40. Let E be a nonempty subset of R that is bounded above. Prove that ifa = sup E, then a EE.Exercise 6.41. Let E be a nonempty set in Rn. Then the distance of a point x = R¹to E is defined bydist (x, E) = inf {||x - y|| : y € E}.Prove the following:

This is the question of topology.

Answered: Exercise 6.40. Let E be a nonempty…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 28E: 28. Let where and are nonempty. Prove that has the property that for every subset of if...

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Exercise 6.40. Let E be a nonempty subset of R that is bounded above. Prove that if a = sup E, then a EE.