Unformatted text preview: open set de&nition of connectedness: a. Prove that if X is compact then f ( X ) , the image of f , is compact. b. Prove that if X is connected then f ( X ) , the image of f , is connected. 6. Upper Hemicontinuous Let F : C & R p ! R 1 be a continuous function, where C ± R 1 . Let &( ! ) = f x 2 R n : F ( x;! ) = g be a correspondence. Show directly from the de&nition that if C is compact, then & is an upper hemicontinuous correspondence. (Hint: The proof is by contradiction. Suppose that & is not upper hemicontinuous at some ! ; this tells you that there is a sequence ! n ! ! with certain properties.) 1...
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- Summer '08
- Topology, Continuous function, Metric space, Cauchy Sequence Suppose