Introduction to Topology

Homework 1

Part I: Prove Theorems 1.2, 1.4, 1.5, 1.9.
Part II: Section 1.1 Exercises # 1(d), 2, 3, 4, 6, 7.

Homework 2

Part I: Prove Theorems 2.3, 2.4.
Part II: Section 1.2 Exercises # 7(a). Section 1.3 Exercises # 1(a,b).

Homework 3

Part I: Prove Theorem 4.2.
Part II: Section 1.4 Exercises # 1, 3. Section 1.5 Exercises # 3.

Homework 4

Part I: Prove Theorem 6.1.
Part II: Section 1.6 Exercises # 5, 6, 7(Just prove the image of f is a compact subset of Y.), 8. Section 2.1 Exercises # 1, 2, 5, 7, 8.

Homework 5

Part I: Prove Theorems 2.2, 3.3.
Part II: Section 2.2 Exercises # 3. Section 2.3 Exercises # 2. Section 2.4 Exercises # 3.

Homework 6

Part I: Prove Theorem 5.1, Lemma 6.3.
Part II: Section 2.5 Exercises # 1.

Homework 7

Part I: Prove Theorems 8.1, 8.2, 9.2, 10.5.
Part II: Section 2.9 Exercises # 1, 3 (replace “a map” by “continuous”).

Homework 8

Part I: Prove Theorems 13.2, 13.3.
Part II: Section 2.13 Exercises # 1.