Math 445: Introduction to Topology I

Emily Dumas

University of Illinois at Chicago
Fall 2015

Textbook	Topology, 2ed, by James R. Munkres. (Prentice Hall, 2000)
Lectures	MWF 1:00pm in 204 Taft Hall
Email	ddumas@math.uic.edu
Office hours	Wednesday and Friday, 9:30-10:30am
Office	503 SEO
CRN	13713, 20457

Handouts

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

Online resources

• Notes on the Tychonoff theorem by Pete L. Clark
• Fractals and Self Similarity by J. Hutchinson
• Dynamical Systems by S. Sternberg, Dover Publications, 2010.
• A Course in Metric Geometry by D. Burago, Y. Burago, and S. Ivanov, AMS Graduate Studies in Mathematics 33, 2001.

About the final exam

The final exam will be held on Monday, December 7, 1:00-3:00pm in 204 Taft Hall.

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 length and difficulty of the final exam problems will be similar to those of the homework and the midterm exam.

Reading

After finishing our discussion of the Arzela-Ascoli-Frechet theorem and the compact-open topology, we will cover as many of the following topics as the remaining class time allows:

• 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

• 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.

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