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Unformatted text preview: 1. Prove that p is an accumulation point of the set E if and only if there exists a sequence of distinct points in such that 2. Verify that 3. Suppose is continuous and for all numbers of the form , , it follows that . Prove that for all x . 4. Prove that given by is uniformly continuous on but not on . 5. Prove directly (Do not use Heine-Borel): If K is compact, F is closed, and , then is compact. 6. Suppose K is compact. Prove that every sequence of points in K has a convergent subsequence whose limit is in K ....
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This note was uploaded on 12/13/2011 for the course MATH 115 taught by Professor Plotkin during the Spring '08 term at Rutgers.
- Spring '08