Unformatted text preview: . 10. Theorem. A set is compact iﬀ it is sequentially compact. 11. Theorem. If E is a compact set and f : E → R is continuous, then f is uniformly continuous . 12. Theorem. If E is a compact set and f : E → R is continuous, then f ( E ) is compact . 13. The other theorems are useful, but you will not need to be able to reproduce them on an exam. However you will need to be able to use them when writing a proof. 14. Extreme Value Theorem . 15. Bolzano’s Theorem . 16. Intermediate Value Theorem ....
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 Spring '07
 thieme
 Topology, Continuous function, Metric space, Compact space, General topology, Heine Borel Theorem.

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