# Math 351: Elementary Topology I

# Section 4, Fall 2012

### Prof. Bert Guillou

**email:**bertguillou ♠ uky ♦ edu

**Phone:**(859) 257-4781

**Office:**773 POT

**Office Hours:**Monday, 10-11 and 3-4.

### Schedule

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

Lecture 1: Introduction, 0.4. | Aug. 22 |

Lecture 2: Open sets in R: 0.4. ^{n} | Aug. 24 |

Lecture 3: Closed sets in R, Topological spaces: 0.4, 1.1. ^{n} | Aug. 27 |

Lecture 4: Topological spaces, examples of topologies on R, injections/surjections/bijections: 0.6, 1.1. HW1 due | Aug. 29 |

Lecture 5: Finite/infinite/countable sets, the cofinite topology on R: 0.6, 1.1, 1.2. | Aug. 31 |

Lecture 6: Reviewed HW1, examples of bases | Sept. 5 |

Lecture 7: Generating a topology from a basis HW2 due | Sept. 7 |

Lecture 8: Reviewed HW2 | Sept. 10 |

Lecture 9: Hausdorff spaces, closures, and interiors HW3 due | Sept. 12 |

Lecture 10: Reviewed HW3, examples of closure and interior | Sept. 14 |

Lecture 11: Boundaries, limits of sequences | Sept. 17 |

Lecture 12: Limits of sequences, WorksheetHW4 due | Sept. 19 |

Lecture 13: Reviewed HW4, Accumulation points | Sept. 21 |

Lecture 14: Reviewed WS1, Subspaces | Sept. 24 |

Lecture 15: Subspaces, Worksheet and SolutionsHW5 due | Sept. 26 |

Lecture 16: Reviewed HW5, Continuous functions | Sept. 28 |

Lecture 17: Continuous functions | Oct. 1 |

Lecture 18: Continuous functions, Worksheet and Solutions HW6 due | Oct. 3 |

Lecture 19: Reviewed HW6, Continuous functions | Oct. 5 |

Review Worksheet and Solutions | Oct. 8 |

Exam review | Oct. 10 |

Exam 1. Letter grades | Oct. 12, in class |

Lecture 20: Reviewed Exam 1, Homeomorphisms | Oct. 15 |

Lecture 21: Homeomorphisms | Oct. 17 |

Lecture 22: Product topology, Worksheet and SolutionsHW7 due (Optional) | Oct. 19 |

Lecture 23: Reviewed WS5, Examples of products | Oct. 22 |

Lecture 24: Embeddings of the torus and cylinder, Worksheet and Solutions HW8 due | Oct. 24 |

Lecture 25: Reviewed HW8 and WS6, Examples of quotients | Oct. 26 |

Lecture 26: Quotient topology | Oct. 29 |

Lecture 27: General quotient topology, Worksheet | Oct. 31 |

Lecture 28: Reviewed HW9 and WS7 HW9 due | Nov. 2 |

Lecture 29: Quotients: the torus, the Klein bottle, and RP ^{2} | Nov. 5 |

Lecture 30: Unions, connected sums | Nov. 7 |

Review worksheet and Solutions HW10 due | Nov. 9 |

Exam review | Now. 12 |

Exam 2 Letter grades | Nov. 14, in class |

Lecture 31: Metric spaces | Nov. 16 |

Lecture 32: Properties of metric spaces | Nov. 19 |

Lecture 33: Connectedness | Nov. 26 |

Lecture 34: Connectedness of products, IVT Worksheet and Solutions HW11 due | Nov. 28 |

Lecture 35: Compactness Test corrections due | Nov. 30 |

Lecture 36: Compactness of [a,b] | Dec. 3 |

Lecture 37: Heine-Borel Theorem, IVT Worksheet and Solutions | Dec. 5 |

Review worksheet | Dec. 7 |

FINAL EXAM!! | Dec 12, 1:00 PM |