# Math 432: Set Theory and Topology

### Bert Guillou

**email:**bertg ♠ illinois ♦ edu

**Phone:**(217) 244-0286

**Office:**330 Illini Hall

**Office Hours:**Wednesday, 3-4:30.

### Schedule

Assignment | Date |
---|---|

Lecture 1: 1.1, 1.2 Suggested Problems: 1.1: 1, 2, 3, 5, 7, 8
| Jan. 20 |

Lecture 2: 1.2, 1.3 Suggested Problems: 1.2: 1, 4, 7, 10; 1.3: 3, 4, 5, 8
| Jan. 22 |

Lecture 3: 1.3, 1.4 Suggested Problems: 1.4: 1, 2, 3, 9, 14 | Jan. 25 |

Lecture 4: 1.3, 1.4 | Jan. 27 |

Lecture 5: 1.5, 2.1 Suggested Problems: 1.5: 1, 4; 2.1: 1, 2, 14 | Jan. 29 |

Homework 1: 1.2: 5, 6, 7a, 8a; 1.3: 1, 9, 11, 12 | due Jan. 29, in class |

Lecture 6: 2.1, 2.2 Suggested Problems: 2.2: 1, 4 | Feb. 1 |

Lecture 7: 2.2, 2.3 Suggested Problems: 2.3: 1 | Feb. 3 |

Lecture 8: 2.3 Suggested Problems: 2.3: 2, 3, 5 | Feb. 5 |

Homework 2: 1.4: 5, 6, 10, 16 1.5: 2, 3; 2.1: 3, 10 | due Feb. 5, in class |

Lecture 9: 2.3, 2.4 | Feb. 8 |

Lecture 10: 2.5, 2.6 Suggested Problems: 2.5: 1; 2.6: 1, 3, 5 | Feb. 10 |

Lecture 11: 2.6, 3.1 Suggested Problems: 2.6: 2, 6; 3.1: 1, 3 | Feb. 12 |

Homework 3: 2.2: 2, 3, 5 2.3: 2, 4, 6; 2.4: 1, 2 | due Feb. 12, in class |

Lecture 12: 3.1 Suggested Problems: 3.1: 6, 9, 10 | Feb. 15 |

Lecture 13: 3.1, 3.4, 3.2 Suggested Problems: 3.2: 1; 3.4: 1
| Feb. 17 |

Lecture 14: 3.2 | Feb. 19 |

Homework 4: 2.5: 2; 2.6: 2, 3, 4, 7, 8; 3.1: 2, 4(a), 5 | due Feb. 19, in class |

Lecture 15: 3.2 | Feb. 22 |

Lecture 16: 3.3 | Feb. 24 |

Lecture 17: 4.1, 4.2 Suggested Problems: 4.1: 2, 3, 10, 17, 20
| Feb. 26 |

Homework 5: 3.1: 6, 7, 9; 3.2: 2; 3.3: 1, 5, 6
| due Feb. 26, in class |

Lecture 18: 4.2, 4.3 Suggested Problems: 4.2: 1, 2, 9; 4.3: 1, 2, 6
| Mar. 1 |

Exam 1: Ch. 1-3 | Mar. 3, in class |

Lecture 19: 4.3, 4.4 Suggested Problems: 4.3: 7, 9, 16; 4.4: 1, 2, 6, 8
| Mar. 5 |

Lecture 20: 4.4
| Mar. 8 |

Lecture 21: 5.1 Suggested Problems: 5.1: 2
| Mar. 10 |

Lecture 22: 5.1 Suggested Problems: 5.1: 7, 10, 11
| Mar. 12 |

Homework 6: 4.1: 3, 12; 4.2: 2, 3; 4.3: 1, 3, 6, 9, 13
| due Mar. 12, in class |

Lecture 23: 5.1
| Mar. 15 |

Lecture 24: 5.1
| Mar. 17 |

Lecture 25: 5.1, 6.1, 5.2 Suggested Problems: 5.2: 1, 2; 6.1: 1
| Mar. 19 |

Homework 7: 4.4: 1, 6, 10; 5.1: 2, 4, 8, 10
| due Mar. 19, in class |

Lecture 26: 5.2
| Mar. 29 |

Lecture 27: 5.2
| Mar. 31 |

Lecture 28: 5.3
| Apr. 2 |

Homework 8: 6.1: 1, 3(a), 4; 5.2: 1, 3, 4, 8, 9
| due Apr. 2, in class |

Lecture 29: 5.3
| Apr. 5 |

Lecture 30: 5.3
| Apr. 7 |

Lecture 31: Definition of topological space
| Apr. 9 |

Homework 9: 5.3: 1, 2, 3, 4, 7, 9, 16; Extra problem: Suppose A _{i} are connected subsets of a metric space X and that the intersection ∩ A_{i} is nonempty. Show that the union ∪ A_{i} is connected.
| due Apr. 9, in class |

Lecture 32: Order topology, Closed sets, Hausdorff spaces
| Apr. 12 |

Lecture 33: Continuous maps, homeomorphisms, subspace topology
| Apr. 14 |

Exam 2 : Ch. 4 and 5 | Apr. 16, in class |

Lecture 34: Connectedness, Path-connectedness
| Apr. 19 |

Lecture 35: Compact spaces
| Apr. 21 |

Lecture 36: The (finite) product topology
| Apr. 23 |

Homework 10 | due Apr. 23, in class |

Lecture 37: The (finite) product topology, continued
| Apr. 26 |

Lecture 38: The box and product topologies
| Apr. 28 |

Lecture 39: Tychonoff's theorem
| Apr. 30 |

Homework 11 | due Apr. 30, in class |

Lecture 39: The Stone-Cech compactification
| May 3 |

Lecture 39: The one-point compactification
| May 5 |

FINAL EXAM!! | May 13, 8:00-11:00 AM |

Department of Mathematics College of Liberal Arts and Sciences University of Illinois at Urbana-Champaign 273 Altgeld Hall, MC-382 1409 W. Green Street, Urbana, IL 61801 USA Department Main Office Telephone: (217) 333-3350 Fax (217) 333-9576 |