### General

This is the webpage for the course Toplogy (V63.0375) in fall 2010, taught
by Sonal Jain (email: *lastname* at cims dot nyu dot edu).

The regular meeting time is on Tuesdays and Thursdays from 2-3:15pm in
Warren Weaver Hall 317. Office hours will be Tuesdays from 3:30-5pm in WWH 619.

Prerequisites: Analysis I or equivalent.

Your grade will be based on ten homework assigments (40%), a midterm exam
(20%), and a take home final exam (40%).

### Syllabus and references

Set theory, topological spaces, connectedness, compactness, countability
and separation axioms, the fundamental goup,
covering spaces, applications.
The official text is Topology by Munkres.

### Lectures

- (9/7) Naive set theory
- (9/9) Axiom of choice, well ordered sets
- (9/14) Topological spaces, bases;
- (9/16) Order, product, subspace topologies;
- (9/21) Closed sets, limit points, Hausdorff axiom
- (9/23) Continuous functions, homeomorphisms
- (9/26) Product topology, Box topology
- (9/28) Metric Spaces
- (10/5) Metric topology, boundedness, uniform topology
- (10/7) Uniform convergence
- (10/12) Connected spaces
- (10/14) Connected subsets of the real line
- (10/19) Compactness
- (10/21) Compactness cont.
- (10/26) Midterm Exam
- (10/28) Recap
- (11/2) Compact subsets of the real line
- (11/4) Limit point compactness, sequential compactness
- (11/9) Local compactness
- (11/11) Countability axioms
- (11/16) Separation axioms
- (11/18) Normal spaces, Urysohn lemma
- (11/23) Urysohn metrization theorem
- (11/30) Quotient topology
- (12/2) Topological groups
- (12/7) Homotopy of paths, fundamental group
- (12/9) Covering spaces
- (12/14) Fundamental theorem of algebra, Borsuk-Ulam theorem.

### Assignments

All dates posted below are DUE dates.
- (9/14) Problem Set 1
- (9/23) Problem Set 2
;
- (9/30) Problem Set 3
- (10/7) Problem Set 4
- (10/19) Problem Set 5
- (11/9) Problem Set 6
- (11/16) Problem Set 7
- (12/2) Problem Set 8
- (12/17) Final