1. MAT 3749 Introduction to Analysis
Section 1.3 Part III
Closed Sets

2. References
Howland, Appendices A-C

3. Goals
Closed Sets
Compact Sets
Extreme Value Theorem (Proof)

4. Closed Sets

5. Example 1

6. Example 1

7. Example 1

8. Example 1

9. Example 1

10. Example 1

11. Theorem

12. Open Cover, Finite Subcover, & Compact Sets

13. Example 2

14. Example 2

15. Example 2

16. Heine-Borel Theorem

17. Extreme Value Theorem

18. Analysis – Fill in the Blanks (Split into 2 groups. Take turn.)

19. Extreme Value Theorem

20. HW
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