Topics to
think about
before Tuesday here
p194
#5,6.
p199 #3, 4
p205 # 1, 5, 6
Below is a list of suggested problems not mandatory.
p199 #9
p205 #7 Homework is
always due on
Tuesdays

Compactness -
Paracompactness
Connectedness -
Produc spaces
(Chapters 3 and 5, Overview of Chapter 6)

Sept 30

Tietze Extension Theorem
Mention of Local Finiteness, Paracompactness and
Nagata-Smirnov
Metrization Theorem,

23, 24

Oct
5

Connected
spaces -
Connected subspaces of the real
line
Components and local
connectedness

24, 25

5

p118 #6, 7
p213 #3, 4
p218 #8
p223 #5,
p248 #6
Also, the problem about tangent disk topology here
There are 8 problems.

Oct
7

Compact spaces
Compact
spaces
of the real line
Tychonoff Theorem

26, 27, 37

Oct
12

Limit point
compactness,
Sequential compactness
Countable compactness,
Compactness and Metric spaces
Some definitions are here.

Special Lecture
by Dennis
Sullivan -
Covering spaces - Classification
The fundamental group of the circle

p330 #3
p335 #4,5,7
p341 #4,5; p348 #4,5,6
Also, understand the pictures of hte coverings here
Applets for the complex exponential map and the map
z->z^n can be found here

Covering transformations - Here
is an interesting handout by Dror Bar Natan (note that he assumes the
path and homotopy lifting theorems, and that the base spaces of
the coverings are not necesarily connected)

Nov
16

Seifert Van Kampen Theorem
Fundamental group computations