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 Borsuk-Ulam |
54, 55, 57 |
pdf |