David Dumas

University of Illinois at Chicago

Spring 2019

Textbook | Topology, 2ed by James R. Munkres. (Prentice Hall, 2000)UIC library / Google books / Amazon |
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Lectures | MWF at 1pm in 309 Taft Hall |

Instructor email | david@dumas.io |

Instructor office hours | MWF 11am |

CRN | 39509 (undergraduate), 39510 (graduate) |

We will cover chapters 2–4 in the textbook and selected topics from chapters 5–8.

Date/time | Course grade fraction | |

Homework | Most Mondays (see list below) | 50% |
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In-class midterm | Wed Mar 6 | 20% |

Final Exam | Mon May 6 | 30% |

**Homework 0 due Friday January 18**: Read the syllabus**Homework 1, due Monday January 28****Homework 2, due Monday February 4****Homework 3, due Monday February 11**:

Problems 17.11, 17.13, 18.2, 18.4, 18.7, and 18.10 from Munkres**Homework 4, due Monday February 18****Homework 5, due Monday February 25**

Typeset solutions are not required. If writing solutions by hand, please make sure they are legible. Staple homework if it spans several sheets of paper. Write your name and the assignment number (e.g. "Homework 1") at the top of the first page.

Many of the homework problems are assigned directly from the primary textbook (Munkres, 2ed).

- Lecture 1 (Mon Jan 14): Topologies and topological spaces (§13)
- Lecture 2 (Wed Jan 16): The topology determined by a basis (§13)
- Lecture 3 (Fri Jan 18): Recognizing a basis of a topology, comparing topologies (§13)
- Lecture 4 (Wed Jan 23): The product topology (§15)
- Lecture 5 (Fri Jan 25): The subspace topology (§16)
- Lecture 6 (Mon Jan 28): Closed sets and limit points
- Lecture 7 (Wed Jan 30): (class canceled due to weather)
- Lecture 8 (Fri Feb 1): T
_{1}and T_{2}spaces (§17) - Lecture 9 (Mon Feb 4): Continuity (§18)
- Lecture 10 (Wed Feb 6): Homeomorphisms, embeddings, examples of continuous functions (§18)
- Lecture 11 (Fri Feb 8): Criteria for continuity, pasting lemma (§18)
- Lecture 12 (Mon Feb 11): Box and product topologies (§19)
- Lecture 13 (Wed Feb 13): Box and product topologies (continued) (§19)
- Lecture 14 (Fri Feb 15): The metric topology; metric space examples (§19)
- Lecture 15 (Mon Feb 18): Metrics on
**R**^{J}(§19); ε-δ continuity (§20)

- Jan 14: Chapter 2 (and skim Chapter 1)

*Topology*by Klaus Jänich, Springer, 1984.- Chapters 1, 3, 4, 6, 8, and 10 contain material we will cover in math 445.

*Introduction to Topology*, 2ed by Theodore Gamelin and Robert Greene, Dover, 1999.- This book is terse but clearly written. It begins by discussing the topology of metric spaces in some detail, introducing general topological spaces a bit later.
- Chapters 1 and 2 contain material we will cover in math 445.