hw2 - E has a subsequence that converges to a point in E....

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Math 240A: Real Analysis, Fall 2011 Homework Assignment 2 Due Friday, October 7, 2011 1. Let X be a complete metric space and E a non-empty subset of X. Prove that E is closed if and only if E is complete. 2. Let X be a metric space and E a compact subset of X . Prove the following: (a) Any sequence in
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Unformatted text preview: E has a subsequence that converges to a point in E. (b) E is closed and totally bounded. 3. Exercise 4 on page 24. 4. Exercise 6 on page 27. 5. Exercise 8 on page 27. 6. Exercise 9 on page 27. 7. Exercise 10 on page 27. 8. Exercise 17 on page 32....
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This note was uploaded on 12/11/2011 for the course MATH 240a taught by Professor Rothschild,l during the Fall '08 term at UCSD.

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