Math 54, Summer 2021
Topology I

Day

Date

Section(s)

Topic(s)

1

Jun 25 (Fri)

1–6

Introduction, set theory

2

Jun 26 (Sat)

7, 12

Special class. Cardinality, topological spaces

3

Jun 28 (Mon)

13

Bases I

4

Jun 30 (Wed)

13

Bases II

5

Jul 2 (Fri)

14, 15

The order topology, the product topology on X x Y

Jul 5 (Mon)

No class. Independence Day (Observed)

Jul 6 (Tue)

x-hour. Proof-writing workshop

6

Jul 7 (Wed)

16

The subspace topology

7

Jul 9 (Fri)

17

Closed sets

8

Jul 12 (Mon)

17

Limit points and Hausdorff spaces

9

Jul 14 (Wed)

18

Continuous functions

10

Jul 16 (Fri)

19, 20

The product topology, the metric topology I

11

Jul 19 (Mon)

20

The metric topology II

12

Jul 21 (Wed)

21

The metric topology III

13

Jul 23 (Fri)

22

The quotient topology

14

Jul 26 (Mon)

23, 24

Connectedness I

Jul 25 (Sun)
–Jul 27 (Tue)

7, 12–21

Midterm Exam

15

Jul 28 (Wed)

24

Connectedness II, path connectedness

16

Jul 30 (Fri)

25, 26

(Path) components, local (path) connectedness, compactness I

17

Aug 2 (Mon)

26

Compactness II

18

Aug 4 (Wed)

27, 28

The Heine–Borel Theorem, limit point compactness

19

Aug 6 (Fri)

29

Local compactness, compactification I

20

Aug 9 (Mon)

29, 30

Compactification II, the countability axioms I

21

Aug 11 (Wed)

30, 31

The countability axioms II, The separation axioms I

22

Aug 13 (Fri)

31, 32

The separation axioms II,
normal spaces I

23

Aug 16 (Mon)

32, 33

Normal spaces II, the Urysohn Lemma I

24

Aug 18 (Wed)

33

The Urysohn Lemma II

25

Aug 20 (Fri)

34

The Urysohn Metrization Theorem, wrap-up

26

Aug 23 (Mon)

51, 52

The fundamental group I

27

Aug 25 (Wed)

53–55, 58, 68–71, 73, 74, 77

The fundamental group II

Aug 23 (Mon)
–Aug 30 (Mon)

7, 12–34

Final Exam