Math 431/531 Fall 2003

Introduction to topology

Instructor: Professor Sadofsky
Office: Deady 101, x6-5619
Email: sadofsky@darkwing.uoregon.edu
WWW:http://noether.uoregon.edu/~sadofsky/431
Office hours: MF 10-11, T 2-3.
Class times: Deady 301, 9-9:50, Problem session Wednesdays 5-6pm.
Homework: due weekly in class on Fridays.
Exams: We'll have one in-class midterm on Friday, October 31, and our final is scheduled at 10:15 on Friday, December 12th (in our classroom).
Grades: will be based 40% on homework, 20% on the midterm and 40% on the final.
Text: Basic Topology, M. A. Armstrong, Springer. I hope to cover most of the book over the two terms, except for chapters 8 and 9. This text is concise (well, sometimes that means explanations are so brief that they are hard to understand). If you have trouble understanding an idea in this text, I recommend looking at Topology by Jim Munkres, second edition. This is very well written, and less concise than Armstrong's book.
Prerequisites: Students should have Math 315 or the equivalent. For U of O undergraduates, "the equivalent" can mean the honors calculus sequence. Graduate students should have had at least an equivalent analysis course.

Assignments

• Week of 9/29: Read Chapter 1 for culture. Don't worry about the proofs - he doesn't really give any in that chapter. Also start Chapter 2, getting through section 2.2. The following problems are due on October 3:
  
  • Show that if T is a tree, then v(T) - e(T) = 1.
  • Problems 1:6, 7.
  Also week of 9/29: due October 8th: 2: 1ab, 2, 3ab, 4a, 6, 7, 9, 11, 14, 16, 17.
  

• Week of 10/6: Read Chapters 2.3 and 2.4. Due October 17: 2: 4B, 5, 8, 12, 15, 19, 27, 29, 31.
  

• Week of 10/13: Read Chapter 3. Due October 24: 28, 30, 32, 33, 34. 3.1, 3.4, and the 2 problems on handout.
  

• Week of 10/20: Finish Chapter 3.1-3.3. Due October 31: 3: 3, 5, 6, 9, 10, 12, 17.
  

• Week of 10/27: Finish Chapter 3.4-3.6. Due November 7: Problem from handout and 2:18, 3:11, 14, 15, 23.
  

• Week of 11/3: Due November 14: 3: 21, 22, 24, 30, 31, 32 and
  • Suppose X = A U B and either both A and B are open or both A and B are closed. Suppose f:X -> Y is continuous when restricted to A or to B. (Both A and B have the subspace topology from X.) Show f is continuous on X. Give an example where X = A U B, f:X -> Y is continuous on A and on B but not on X.
  • Let X be a metric space. Put the product topology on XxX. Show d:XxX -> R is continuous.
  • Porve that if \beta is a base for the topology on X and \beta' is a base for the topology on Y then the collection \gamma = {BxB': B in \beta and B' in \beta'} is a base for the product topology on XxY.
  
  

• Week of 11/10: Read 4.1, 4.2. Due November 21: 2: 22, 24, 25, 26. 3: 33, 37, 40, 41.
  

• Week of 11/17: Read 4.3. Due November 26: problem from handout. 4: 1, 2, 5, 7, 8, 11.
  

• Week of 11/24: Finish chapter 4. Due December 5: see handout.
  

  For further detail assignments, download the solution sheets above as they become available.

  Handouts

  Note: many of these require Adobe's Acrobat reader (or some other software that can read PDF files, such as xpdf) which is available for free download.
  • Solutions to homework due on October 3.
  • Solutions to homework due on October 8.
  • Solutions to homework due on October 17.
  • Solutions to homework due on October 24.
  • Practice midterm. Solutions to practice midterm.
  • Solutions to homework due on October 31.
  • Solutions to practice midterm.
  • Solutions to midterm, October 31.
  • Solutions to homework due on November 7.
  • Solutions to homework due on November 14.
  • Solutions to homework due on November 21.
  • Solutions to homework due on November 26.
  • Solutions to homework due on December 5.
  • Review sheet for course. Note that I changed this on 12/5 at about 8:45 AM.

Help

Back to my home page.