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Unformatted text preview: . 10. Theorem. A set is compact i 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. Bolzanos Theorem . 16. Intermediate Value Theorem ....
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This note was uploaded on 08/12/2009 for the course MAT 371 taught by Professor Thieme during the Spring '07 term at ASU.
- Spring '07