Math 262 (Winter 2009)

Information

Announcements (16th Jan, 2009)

Course Name: Point set Topology (Math 262) Winter 2009, Section 51
Instructor: Tathagata Basak, office: 315 Eckhart
Classes will be held M-W-F 12:30-1:20pm at room E 206
Office Hours: Monday 2:40-3:30, Friday 3:40-4:30
Course Webpage: http://www.math.uchicago.edu/~tathagat/teaching/09_math262/index.html

College fellow: Daniele Rosso. Ofiice: MS 303 F
Daniele's office hour: Tue, Thu: 4:30 - 6:00.
e-mail:d_rosso@math.uchicago.edu
Problem session: Thursday 6-7 pm at Ry 358 (starting 15th).

I uploaded more problems on Friday evening (16th Jan) for the 2nd homework. Please check the same link again.
From this week the homeworks are due on Friday. So this set will be due on Jan 23.

Course Material

Textbook James R. Munkres, Topology, 2nd Ed.
Couple of other reference:
Syllabus: The course catalog says: This course examines topology of the real line, topological spaces, connected spaces and compact spaces, identification spaces and cell complexes, and projective and other spaces.
For more detail on what is going to happen in the beginning of the course see below in the course log - but the log is going to grow as we progress.
Prerequisites: Course catalog says: Math 20300 or 20700 and 25400 or 25700.
If you are not sure if you have the right prerequisites, PLEASE TALK TO ME IN THE FIRST WEEK OF CLASS.

Course Policy

Homework:
- Homeworks will be posted on the course log at the bottom of this page probably after each day's class.
- Homeworks assigned during one week will be due on the following Friday at the beginning of the class. Please staple your homework.
- Late homework will not be accepted.
- There will be N+1 homeworks, you should submit all of them except the final one. The best N-1 out of the N you submit will count towards the final grade.
Examinations:
- There will be weekly homeworks (30%), one midterm (30%), and the final will be the rest (40%).
- Note to the students and self: Please check the final exam time in the college schedule. Please make sure that you do not have any other engagement at that time.
Important
- The final exam must occur at the time and place designated on the College Final Exam Schedule. In particular no final examinations may be given during the tenth week of the quarter except in the case of graduating seniors. (If this is the case please let me know as soon as possible)
- There will be no makeup exams (quizzes, Midterm or final). Incompletes are rarely given, and only for cases of extreme personal tragedy.

Links

Mathematicians : Euler, Gauss, Poincare, Riemann,

Log

This is to keep track of what has to be covered, what has been covered so far, to remedy the things that I might blotch up in class. This is also where I shall put the homeworks.
I have already started to make up a list below to organize things in my mind. But probably we wont cover everything listed below in the first week - in that case they will spill over to the next week...
The problems that you need to submit are marked with a ($) sign.


Week 1	Homework 1, Some notes (Please let me know if you notice any typoes or more serious mistakes)
A bit of Naive set theory	Cardinality of a set. Finite, Countable and uncountable sets. Cartesian Products Well ordering axiom, and Zorn's lemma. Well ordered sets and Ordinals. Existence of an uncountable well ordered set.

Week 2	Homework 2
Topological spaces	First definitions, open sets and continuous functions. Examples - Topology generated by a sub-basis, order topology, initil topology generated by a set of functions, product topology, subspace topology. Closed sets, limit points..

Week 3	Homework 3
Spaces and Continuous functions (Contd.)	Closure, interior, limit points. Hausdorff spaces/ Continuous functions and homeomorphisms. Metric spaces.

Week 4	Homework 4
Spaces and Continuous functions (Contd.)	More on Metric topology. Quotient topology.

Week 5	Homework 5
Spaces and Continuous functions (Contd.)	More on quotient topology. Glueing spaces by maps. Examples of glueing.
Connectedness	Definition and basic properties. Connected subsets of real line. Path connectedness.

Week 6	Homework 6
Connectedness (Contd.)	Connectedness and Path Connectedness. Components and Path Components
Compactness	Definition and basic properties. Compact subsets of Euclidean space. Compactness in metric spaces. Limit Point compactness and sequential compactness.

Week 7	Homework 7
Compactness	Compactness in metric spaces - equivalent conditions. Local compactness - one point compactification.
Countability and seperation axioms	First and second countable spaces. Dense subsets. Seperation axioms: T_0, T_1, Hausdorff, Regular and normal spaces.

Week 8	Homework 8
Seperation axioms	Criteria for a space to be normal Uryshon's lemma. Tietze extension theorem.

Week ?	Homework ?
Topic	list
topic	list

Tathagata Basak

Last modified: Fri Mar 2 17:52:45 CST 2007