Unformatted text preview: and . For example, and . Consider the function defined by . For what points does f have a limit? Prove your claim. 3. Suppose that (H1) f is a function which is defined and continuous on (H2) g is a function which is defined and continuous on (H3) Define a function h on by Give an proof that h is continuous at 0. 4. Prove directly that is not uniformly continuous on . 5. Prove that if K is compact, then K is closed and bounded. 6. For this problem, you may assume that if K is compact and is continuous, then is compact. Prove that if K is compact and is continuous, then achieves both its supremum and infimum, i.e. prove that f attains a maximum and minimum value....
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 Spring '08
 PLOTKIN
 Topology, Continuity, Continuous function, Metric space, Compact space, Continuous Function Theorem

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