Definitions and Theorems:

Def 6.1 (compact set)

Def 6.17 (sequentially compact set)

Theorem 6.24 (Heine-Borel theorem)

Def 7.1 (connected and disconnected sets)

Def 8.1 (continuous function)

Def 8.10 (limit of a function at a point)

Corollary 8.20 (extreme value theorem)

Def 8.23 (uniformly continuous function)

Corollary 8.28 (intermediate value theorem)

Suggested Review Problems/Exercises:

Section 6:

Exercises: 6.1, 6.2

Problems: 6.1, 6.2, 6.3, 6.5, 6.10. 6.14

Section 7:

Exercises: 7.3, 7.5, 7.6

Problems: 7.4, 7.9

Section 8:

Exercises: 8.3

Problems: 8.1, 8.2, 8.13, 8.15