Please solve number 3 3. Given that (X, d) is a mtric space. Suppose p is another metric onX such that d(x, y) ≤ kp(x, y) for each x, y in X. Then prove that thetopology generated by d is a subcollection of the topology generatedby rho on X.4. Let X be a non-empty set and p E X be a specific point. LetJ = {UC X p E U} U {0}. Answer each of the following:

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Answered: 3. Given that (X, d) is a mtric space.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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3. Given that (X, d) is a mtric space. Suppose p is another metric on X such that d(x, y) ≤ kp(x, y) for each x, y in X. Then prove that the topology generated by d is a subcollection of the topology generated by rho on X.