MAT 3749 Introduction to Analysis Section 1.3 Part III Closed Sets http://myhome.spu.edu/lauw

References Howland, Appendices A-C

Goals Closed Sets Compact Sets Extreme Value Theorem (Proof)

Closed Sets

Example 1

Example 1

Example 1

Example 1

Example 1

Example 1

Theorem

Open Cover, Finite Subcover, & Compact Sets

Example 2

Example 2

Example 2

Heine-Borel Theorem

Extreme Value Theorem

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

Extreme Value Theorem

HW Have a great Thanksgiving!!!