## Math 432. Set Theory and Topology

Instructor Syllabus

**Text: **Irving Kaplansky, *Set Theory and Metric Spaces,* 2nd Edition, 1977.

Chapter 1 - Basic Set Theory1.1 Inclusion 1.2 Operations on Sets 1.3 Partially Ordered Sets and Lattices 1.4 Functions 1.5 Relations; Cartesian Products |
.5 hr. .5 hr. 1 hr. 1 hr. 1 hr. |

Chapter 2 - Cardinal Numbers2.1 Countable Sets 2.2 Cardinal Numbers 2.3 Comparison of Cardinal Numbers; Zorn�s Lemma 2.4 Cardinal Addition 2.5 Cardinal Multiplication 2.6 Cardinal Exponentiation |
2 hr. 1 hr. 3-4 hr. 1 hr. 1 hr. 1-2 hr. |

Chapter 3 - Well-ordering: The Axiom of Choice3.1 Well-ordered Sets 3.2 Ordinal Numbers 3.3 The Axiom of Choice 3.4 The Continuum Problem |
4 hr. 1-2 hr. 3-4 hr. 1 hr. |

Chapter 4 - Basic Properties of Metric Spaces4.1 Definitions and Examples 4.2 Open Sets 4.3 Convergence; Closed Sets 4.4 Continuity |
1 hr. 2 hr. 2-3 hr. 2 hr. |

Chapter 5 - Completeness, Separability, and Compactness5.1 Completeness 5.2 Separability 5.3 Compactness |
4 hr. 2 hr. 2-3 hr. |

Total |
37-43 hr. |

Notes:

- You will need to fit two or three hour exams into the above schedule.
- The text is very readable. Much of the content of the text is in the exercises, so many of the exercises should be covered, either during discussion/problem-solving sessions in class or as work done outside of class.
- This class often has a small enrollment; 10-15 students. It is both possible and very useful to have students present their work at the board on a regular basis.