Unformatted text preview: explicit what you are assuming. Make sure you justify each step. Good luck! 1. Let for all x in R . Verify that 2. Show that given by is uniformly continuous. 3. Suppose is continuous. Let p be a real number. Prove the set is open. 4. Suppose are compact sets in R . Prove that is compact. (You may prove this by any method, but you should know how to prove it directly.) 5. Give an example of an open cover for that has no finite subcover. 6. Suppose is continuous. Prove there exists a point p in such that ....
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 Spring '08
 PLOTKIN
 Topology, Continuity, Continuous function, Metric space, Compact space, Continuous Function Theorem, R. Verify

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