Intro to Topology/ Found to Topology


Lecture: MWF 1400-1450, Location   DSH-233


Instructor: Dimiter Vassilev     Office: SMLC 326 Email:  Phone: 505 277 2136


Math 431 Introduction to Topology & Math 535  Foundations of Topology

Description:  Metric spaces, topological spaces, continuity, algebraic topology.  Basic point set topology. Separation axioms, metric spaces, topological manifolds, fundamental group and covering spaces.


Prerequisite: MATH401


Text: Introduction to Topology, Th. Gamelin & R.E.Greene, Dover Publ., 2nd edition



Office Hours: Monday & Friday 3pm-4pm, Wednesday 10am-11am or by appointment. Feel free to stop-by anytime if you have a quick question.                                                                                                       


Final Exam: Wednesday, December 9, 3:00pm - 5:00pm, please check Final Examination Schedule .

Students having conflicts with this examination schedule must notify the appropriate instructor before Friday, November 6, 2015.




Please note the following guidelines for the course:

Grades: The final grade will be determined by homework & quizzes (25%), two midterms (50%) and a final exam (25%)
.  Exam scores are posted on .


Homework:  Homework from the previous week is due Monday at the beginning of class. There will be one HW weekly. You can work together on the homework, but you do need to write up your own solutions in your own words. To help the grader, please write your solutions up neatly and clearly (no points for work that the reader cannot follow- this is also true for exams), and staple the sheets.   The best ten homework/quiz grades only will be counted for a total of 100pts. Please no late homework.


Missed Exams:  Make-up exams can be arranged for exams missed with a VALID excuse (illness, family emergency, active participation in scholarly or athletic activities), and ONLY if prior notice is given. 


Disability Statement: We will accommodate students with documented disabilities. During the first two weeks of the semester, those students should inform the instructor of their particular needs and they should also contact Accessibility Services in Mesa Vista Hall, Room 2021, phone 277-3506.  In addition, they should see CATS- Counseling and Therapy Services; Student Health Center (277-4537). (They can help if you suffer from exam anxiety).    




                      Homework – Fall 2015  (please check after class as advanced postings of homework could change)

Turn in only the odd numbered problems.





Odd numbered Homework Problems are due

the first class of the following week

1 Aug. 17 1. Metric Spaces - completeness, the Baire category theorem HW1  
2 Aug.  24 Compactness - spaces of continuous functions. HW2  
3 Aug. 31

Principle of uniform boundedness in a Banach space. Contraction principle.

4 Sep. 7 2. Topological Spaces HW4
5 Sep. 14 Continuous function. Base of a topology. HW5 
6 Sep. 21

Separation axioms. Urysohn's lemma and Tietze's  extension theorem. Compactness.

The Arzela-Ascoli theorem.

7 Sep. 28 Connected and path connected space. Locally compact spaces. HW7
8 Oct. 5        
October 8–9
Exam 1, Wednesday  Oct. 7 
Fall Break
Exam scores are posted on
9 Oct. 12 Products of topological spaces - Alexander subbase theorem, Tychonoff's theorem. HW8
10 Oct. 19

3. Quotient spaces, group actions and covering spaces - Hausdorffness of the quotient space;

group action with quotient map a covering; uniqueness of lifts.

11 Oct. 26

The group of deck transformations; the quotient under the group of deck transformations;


12 Nov. 2   HW11
13 Nov. 9

4. Homotopy Theory - the fundamental group. Free products of groups.

The Seiferet - van Kampen theorem.

14 Nov. 16

The Seiferet - van Kampen theorem. Deformation retracts. Homotpic maps and homotopy equivalent spaces,

consequences for the fundamental groups. Brower'r theorem. Covering spaces- lifting of paths and homotpies.

The Monodromy theorem. Fundamental group vs. Aut group of a covering.

15 Nov. 23

November 26-27

Exam 2, Wednesday Nov. 25


16 Nov. 30 Borsuk-Ulam's theorem HW14
  Dec. 7 Finals week Wednesday, December 9, 3:00pm - 5:00pm