Week Starts  Sections  Topics  HW  Assignment (hand in the underlined problems) on Friday.  Remarks 

Aug 24th 
1.1 
Introduction  Administrative details (all
discussed in the syllabus) Point set topology 
0 
Fill this
form. 

Sept 3rd 
2.1 2.2 
Open and closed sets in R^{n}. Relative neighborhoods 
1 
1.1 You do not need to justify your answers in this problem. This
is just to sharpen your topological neurons. Section 2.1 Open and closed sets in R^{n}. 2.1 (problems 1, 4, 5 ,6, 7, 8, 9.) Justify your answers. A. Determine whether the rectangle (0,2)x(0,1) is open and/or closed in R^{2}. Justify your answer. 2.2 2.3  (problems 4, 5 ,6, 7, 8, 9). Justify your answers. 2.4 2.9 2.12 
Sept 3rd, Labor day. 
Sept 10th 
2.3 2.4 
Continuous functions. Compact sets 
2 
Section 2.2 Relative neighborhoods For each of the following terms, down an informal definition and a formal definition. In both cases, use ONLY words and no symbols. The informal definition should be understood by a person with minimal math background (junior high level). Terms: interior point, exterior point, frontier point, limit point, open set, closed set, open set relative to a subset A, closed set relative to a subset A, (A is a subset of the plane), continuous function. In all problems below, justify all your steps. 2.19 2.22 Find the interior and the exterior of the Cantor set. Consider C=[0,1] as a subset of the real line A. Find the interior of C. Consider C=[0,1] as a subset of the Euclidean plane R^2. Find the interior of C. Prove that the intersection of finitely many open set is open. 

Sept 17th 
2.5 
Read this
blog post. Connected sets Special lecture 
3  2.17 Section 2.3 Continuity 2.25 B. Determine whether the function f from the interval [0,1) to the circle, defined by f(t)=(cos(2πt),sin(2πt)) is continuous, and whether the inverse of f is continuous. C. Prove that a constant function from R^{n} to is R^{m }continuous. 2.26 Section 2.4 Compact sets 2.27 2.28 D. Determine whether a circle is a compact subset of R^{2}. 

Sept 24th 
Applications Review 
4 

Oct 1st 
3.2 3.3 3.4 3.5 
Open sets and neighborhoods. What is
"a topology"? Continuous functions between topological spaces. Connectedness and compactness Separation axioms Product spaces Quotient spaces 
5 
Midterm on Wed Oct 3rd 

Oct 8th 
6 
No class Oct 8th 

Oct 15th 
7 

Oct 22nd 
8 

Oct 29th 
9 

Nov 5th 
10 

Nov 12th 
11 
Midterm on Friday Nov 16th  
Nov 19th 
12 
Nov 2224 Thanksgiving 

Nov 26th 
13 

Dec 3rd 
14 

Final 
Final Exam: Wednesday, December 19, 2:15pm5:00pm 
