1. Chapter 7 Quotients

2. Contents:
7.1 The Quotient Topology
7.2 Continuity of a Map on a Quotient
7.3 Identification of a Subset to a Point
7.4 A Necessary Condition for a Hausdorff Quotient
7.5 Open Equivalence Relations
7.6 The Real Projective Space
7.7 The Standard C∞ Atlas on a Real Projective Space
Problems

4. 7.1 The Quotient Topology

6. 7.2 Continuity of a Map on a Quotient

8. 7.3 Identification of a Subset to a Point

11. 7.4 A Necessary Condition for a Hausdorff Quotient

12. 7.5 Open Equivalence Relations

17. 7.6 The Real Projective Space

27. 7.7 The Standard C∞ Atlas on a Real Projective Space

31. Problems
Solution:

37. Solution: