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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.

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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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. 4. Let X be a non-empty set and p E X be a specific point. Let J = {UC X p E U} U {0}. Answer each of the following:
Transcribed Image Text: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. 4. Let X be a non-empty set and p E X be a specific point. Let J = {UC X p E U} U {0}. Answer each of the following:
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