Courses:

Introduction to Topology >> Content Detail



Assignments



Assignments

Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.
There are two kinds of assignments: Weekly exercises that are not to be handed in for grading but are intended to prepare students for the exams, and problem sets that are to be handed in and graded.

Problem Sets

The problem sets are assigned from the textbook: Amazon logo Munkres, James R. Topology. 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 28 December 1999. ISBN: 0131816292.

Problem set 0 is a "diagnostic" problem set. It is designed to determine whether you are comfortable enough with the language of set theory to begin the study of topology. We will grade it in class at the second session. lf you miss more than 8 answers, you should probably take another proof-based course before trying this one. The grade on this problem set is intended for advising purposes only.

For problem sets 1-4, the solutions are to be written out carefully and legibly, in good mathematical style. "Careful" has an obvious meaning. "Legible" means to do it in LATEX or (if handwritten) in ink and double-spaced. "Good mathematical style" means the style demanded by editors of math journals. Please read these comments about what the mathematics profession means by "good mathematical style (PDF)." Follow them!

Note well: your first written solutions constitute your first draft; this is not acceptable. It will need to be rewritten, to clean up grammar and sentence structure and exposition. Treat it like a paper in a humanities class. (Unless you hand in sloppy papers there too!)

PROBLEM SETSDESCRIPTION
Problem Set 0Sec. 1; 2. Give answers only. Your answers to (j), (k), and (l) should be "yes" or "no." Your answers to the others should be one of the following:
⇒, , ⇔, ⊂, ⊃, =

Sec. 1; 5. Give answers only

Sec. 2; 4c and 4e. Give answers only
Problem Set 1Sec. 3; 13

Sec. 9; 8

Sec. 13; 7 and sec. 17; 16. Give answers only

Sec. 17; 18. Give answers only
Problem Set 2Sec. 18; 13

Sec. 20; 6ab

Sec. 20; 8bc, Assume 8a. Give answers only in 8c

Sec. 24; 4
Problem Set 3Sec. 26; 9

Sec. 26; 12

Sec. 28; 4

Sec. 30; 5
Problem Set 4Sec. 31; 7abd

Sec. 33; 4

Sec. 34; 4 and 5. Give proofs or counterexamples

Sec. 38; 9
Problem Set 5(PDF)


Weekly Exercises

The exercises are assigned from the textbook: Amazon logo Munkres, James R. Topology. 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 28 December 1999. ISBN: 0131816292. Collaboration on the weekly exercises is encouraged; you can learn a good deal from your fellow students. But the work on the problem sets is to be strictly your own. If you can't do all of a problem, do what you can and write "here's where I got stuck" "Faking it" is much worse than saying "I couldn't do it."

WEEK #TOPICSEXERCISES
1Logic and FoundationsSec. 1; 3

Sec. 2; 1, 2, 4, 5
2Relations, Cardinality, Axiom of ChoiceSec. 3; 11, 12, 15

Sec. 5; 4, 5

Sec. 6; 3, 6

Sec. 7; 3, 4, 5
3Topologies, Closed SetsSec. 7; 6

Sec. 13; 2, 6, 8

Sec. 16; 3, 4, 8, 10

Sec. 17; 3, 4, 5, 6, 8, 9
4Continuous Functions, Arbitrary ProductsSec. 17; 10, 11, 12

Sec. 18; 2, 3, 7, 8

Sec. 19; 1, 2, 3, 6, 8
5Metric TopologiesSec. 19; 7

Sec. 20; 2, 4, 5, 8a

Sec. 21; 3, 4, 6, 7
6Quotient TopologySec. 22; 2, 3, 6
7Connected Spaces, Compact SpacesSec. 23; 2, 3, 5, 7, 8

Sec. 24; 1, 5, 8, 9

Sec. 25; 1, 2, 3

Sec. 26; 1, 4, 5, 6
8More about CompactnessSec. 26; 7, 8

Sec. 27; 1, 4

Sec. 28; 1, 2, 3
9Well-ordered Sets, Maximum Principle

Midterm Exam
10Countability and Separation AxiomsSec. 10; 2, 3, 6

Sec. 29; 5, 6, 7, 8

Sec. 30; 1, 2, 4 7, 8, 9
11Urysohn Lemma, MetrizationSec. 31; 1, 3, 6

Sec. 32; 1, 2, 3, 6, 7
12Tietze TheoremSec. 33; 2, 6, 7, 8
13Tychonoff Theorem, Stone-Cech CompactificationSec. 34; 1, 3, 7, 8

Sec. 37; 2, 3

Sec. 38; 5, 6
14Baire Spaces, Dimension TheorySec. 38; 3, 4

Sec. 36; 1, 5

Sec. 48; 1, 2, 3, 5, 6
15Imbedding in Euclidean Space
Final Exam

 








© 2010-2021 OpenCollege.com, All Rights Reserved.
Open College is a service mark of AmeriCareers LLC.