*Test 1 took place on February 14 in UH/213 at 2:30pm. It covered material up through section 19 in the te**xtbook (product and box topologies). Recommendation: study problems from Assignments 1,2, and 3 from the relevant sections.*- Study sheet for test 1
*Test 2 will take place on March 22 in HH/109 at 2:30pm. It will cover material from sections 20, 21, and 23--28 in the te**xtbook. This includes metric topologies, connectedness, and compactness, spaces. Recommendation: study problems from Assignments 3, 4, and 5 from the relevant sections.**Study sheet for test 2**The***Final****Exam**will take place on**April 24****in****MDCL 1110**at**4****:****0****0pm**. You can expect 8 to 10 problems, roughly twice as long as Test 2. It is comprehensive and covers chapters 1--4 from the text book, with an emphasis on the assigned sections covered in lectures. The key sections are 1--3, 5--7, 12--21, 23--34. Note that the final exam will**not**cover section 22 (quotient topology), and it will**n****ot**cover sections 35 or 36 (Tychonoff Theorem and Stone-Cech compactification).*The main topics are to review are: topologies, basis for topology, ordered sets and the order topology, subspaces and products, closed sets and limit points, metric spaces,**connectedness and connected components, path connected and path components, compactness, limit point compactness, separation axioms (T_1, Hausdorff, regular, normal), first and second countability, compactification and metrization. Below is a study sheet with many suggested problems, and note that the study sheet is longer than the final exam will be.*

*Study sheet for final exam*

A student's grade will be determined by Homework, Quizzes, Midterms, and the Final Exams according to the following percentages:

20% Homework

20% Midterm 1(February 12, 2:30--3:20pm, HH/109)

20% Midterm 2 (March 22, 2:30--3:20pm, HH/109)

40%Final Exam (April 24, 4:00--6:30pm, MDCL 1110)

All assignments from course textbook:

Topology, second edition, by James R. Munkres (Prentice Hall, 2000).

1.Assignment 1 due Thursday, January 24

ReadingProblemsProblems (to be handed in)

Chapter 1

Sections 1--3

Sections 5--7

p.15 # 3

p.28 # 3

p.44 # 2

p.51# 5

p.15 # 8

p.28 # 4

p.44 # 6

p.51 # 1, 4## Solutions to Assignment 1

2.Assignment 2 due Thursday, January 31

ReadingProblemsProblems (to be handed in)

Chapter 2

Sections 12--16

Sections 17--18

p.83 # 1, 5

p.92 # 9

p.100 # 1, 7

p.111 # 6, 12

p.83 # 4, 8

p.92 # 4, 10

p.100 # 6, 8

p.111 # 3, 4, 9ab

## Solutions to Assignment 2

3.Assignment 3 due Thursday, February 14

ReadingProblemsProblems (to be handed in)

Chapter 2

Section 19

Section 20

p.101 # 5, 12, 15

p.111 # 2

p.118 # 5

p.126 # 2, 3

p.101 # 10, 13

p.118 # 6, 7

p.127 # 4, 5

## Solutions to Assignment 3

4.Assignment 4 due Tuesday, March 12

ReadingProblemsProblems (to be handed in)

Chapter 2

Section 21

Chapter 3

Sections 23, 24, 26

p.133 # 2, 6

p.152 # 2

p.170 # 2, 3, 4

p.133 # 1, 8, 9

p.152 # 3, 5

p.157 #2, 3, 9

p.170 # 5, 6, 8

## Solutions to Assignment 4

5.Assignment 5 due Friday, March 22

ReadingProblemsProblems (to be handed in)

Chapter 3

Section 25

Sections 27--29

p.177 # 5, 6

p.162 # 2

p.177 # 3, 4

p.181 # 3, 6

## Solutions to Assignment 5

6.Assignment 6 due Tuesday, April 9

ReadingProblemsProblems (to be handed in)

Chapter 2

Section 22

Chapter 4Sections 30--34

p.145 # 5

p.194 # 2, 8

p.199 # 3, 7

p.205 # 4, 5, 7

p.212 # 1, 2b

p.218 # 3

p.194 # 4, 5

p.199 # 2, 5

p.205 # 1, 2, 3

p.212 # 2a

p.218 # 1