Day 
Topics 
Book sections 
Notes 
9/12 
introduction 

pdf 
9/15 
topological spaces, continuous maps, bases 
12, 13 
pdf 
9/19 
more on bases, subbases 
13 
pdf 
9/22 
subspace and product topology 
15, 16 
pdf 
9/26 
order topology, closed sets, closure 
14, 17 
pdf 
9/29 
limit points, some separation axioms (Hausdorff = T2, T1), more on continuity 
17, 18 
pdf 
10/3 
more on continuity, homeomorphisms 
18 
pdf 
10/6 
product topology in general 
19 
pdf 
10/10 
(Thanksgiving, no class) 


10/13 
metric topology 
20, 21 
pdf 
10/17 
connectedness 
23, 24 
pdf 
10/20 
more on connectedness, path connectedness 
23, 24 
pdf 
10/24 
compactness 
26, 27 
pdf 
10/27 
Term Test 


10/31 
more on compactness 
26, 27 
pdf 
11/3 
compactness in metric spaces 
27, 28, 45 
pdf 
11/7 
(Fall break, no class) 


11/10 
compactness (end), the Cantor set 
27, 28, 45 
pdf 
11/14 
separation axioms: T3, T4 
31, 32 
pdf 
11/17 
more on separation axioms, Urysohn's lemma 
31, 32, 33 
pdf* 
11/21 
Tietze extension theorem 
35 
pdf 
11/24 
Tychonoff's theorem: Micheal's notes 
37 
pdf 
11/28 
homotopy of paths 
51 
pdf 
12/1 
more on homotopy, fundamental group, case of circle (beginning) 
51, 52, 53, 54 
pdf* 
12/5 
fundamental group of circle (conclusion), Brouwer fixed point and BorsukUlam 
54, 55, 57 
pdf 