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Math 360 Homework 3: Problems from Rudin's Principles of Mathematical Analysis, Assignments of Mathematics

University of Pennsylvania (UPenn)Mathematics

Ten exercises from chapter 2 of rudin's principles of mathematical analysis for a university-level mathematics course. The exercises cover topics such as subsets of metric spaces, open sets, and countable sets.

Typology: Assignments

2009/2010

Uploaded on 03/28/2010

koofers-user-406 🇺🇸

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Download Math 360 Homework 3: Problems from Rudin's Principles of Mathematical Analysis and more Assignments Mathematics in PDF only on Docsity! 1 (Math 360) Homework 3: Due February 5, 2009 All numbered exercises are from Rudin’s Principles of Mathematical Analysis. Exercise 1: Let A1, A2, . . . be subsets of a metric space. (a) Suppose Bn = ⋃n i=1 Ai. Prove Bn = ⋃n i=1 Ai (b) If B = ⋃∞ i=1 Ai prove B ⊃ ⋃∞ i=1 Ai (c) Given an example where B 6= ⋃∞ i=1 Ai Exercise 2: Suppose (X, d) is a metric space and E ⊆ X is any subset. Show that there is a subset Y of X such that E is open in (Y, d). Exercise 3: Chapter 2, Exercise 6. Exercise 4: Chapter 2, Exercise 9. Exercise 5: Chapter 2, Exercise 14. Exercise 6: Chapter 2, Exercise 15. Exercise 7: Chapter 2, Exercise 16. Exercise 8: Chapter 2, Exercise 21. Exercise 9: Chapter 2, Exercise 22. (Recall a set is countable if there is a bijection between it and N). Exercise 10: Chapter 2, Exercise 23. Exercise 11: Chapter 2, Exercise 25.

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Math 360 Homework 3: Problems from Rudin's Principles of Mathematical Analysis, Assignments of Mathematics

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