David Dumas

University of Illinois at Chicago

Fall 2015

Textbook | Topology, 2ed, by James R. Munkres. (Prentice Hall, 2000) |
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Lectures | MWF 1:00pm in 204 Taft Hall |

ddumas@math.uic.edu | |

Office hours | Wednesday and Friday, 9:30-10:30am |

Office | 503 SEO |

CRN | 13713, 20457 |

- Course Syllabus
- Solution to P1 from Homework 4
- Practice Midterm
- Midterm (as given on October 14)
- Midterm Solutions

The exam will have a total of **six** problems, of which students will be required to complete any **four**.

The exam will be cumulative. There will be some emphasis on material covered since the first exam.

At least two of the problems on the final will be "very familiar", in the following sense:

- At least one problem will be taken from a previous homework assignment
- At least one problem will be a minor variation of a problem on the midterm exam

- The Hausdorff distance on subsets of a metric space
- Problem 45.7 in Munkres
- Section 7.1 in Sternberg

- Applications of the Hausdorff distance
- Hutchinson's theorem, as in Chapter 7 of Sternberg or Hutchinson
- Gromov-Hausdorff convergence of metric spaces, as in Section 7.3 of Burago-Burago-Ivanov

- Construction of a space-filling curve
- Section 44 in Munkres

- The Baire Category Theorem and applications
- Sections 48-49 in Munkres

- Homework 1 is due Monday, August 31.
- Homework 2 is due Wednesday, September 9.
- Homework 3 is due Monday, September 14.
- Homework 4 is due Monday, September 21.
- Homework 5 is due Wednesday, September 30.
- Homework 6 is due Wednesday, October 7.
- Homework 7 is due Monday, October 19.
- Homework 8 is due Wednesday, October 28.
- Homework 9 is due Friday, November 6.
- Homework 10 is due Monday, November 16.
- Homework 11 is due Wednesday, November 25.
- Homework 12 is due Friday, December 4.