Intro to Topology/ Found to Topology
Instructor: Dimiter Vassilev Office: SMLC 326 Email: vassilev@unm.edu 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., 2^{nd} edition
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
https://learn.unm.edu/ .
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: Makeup 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 2773506. In addition, they should see CATS
Counseling and Therapy Services;
Homework – Fall 2015 (please check after class as advanced postings of homework could change)
Turn in only the odd numbered problems.
Week 
Date 
Topics 
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. 
HW3 
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 ArzelaAscoli theorem. 
HW6 
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 https://learn.unm.edu/ 
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. 
HW9 
11  Oct. 26 
The group of deck transformations; the quotient under the group of deck transformations; examples 
HW10 
12  Nov. 2  HW11  
13  Nov. 9 
4. Homotopy Theory  the fundamental group. Free products of groups. The Seiferet  van Kampen theorem. 
HW12 
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. 
HW13 
15 
Nov. 23 November 2627 
Exam 2, Wednesday Nov. 25 Thanksgiving 

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