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 *Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? Kai   *Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? Kai 
 ** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course.   ** Indeed so, though usually when talking about boundedness, people use the letter <math>M</math> and not the letter <math>\epsilon</math>. It makes no difference, of course. 
− 
 
−  ===Solution===
 
−  [http://katlas.math.toronto.edu/drorbn/images/7/77/10327a501.JPG page1]
 
−  [http://katlas.math.toronto.edu/drorbn/images/7/7e/10327a502.JPG page2]
 
−  [http://katlas.math.toronto.edu/drorbn/images/6/6b/10327a503.JPG page3]
 
−  [http://katlas.math.toronto.edu/drorbn/images/6/61/10327a504.JPG page4]
 
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−  [http://katlas.math.toronto.edu/drorbn/images/c/c6/10327a506.JPG page6]
 
−  [http://katlas.math.toronto.edu/drorbn/images/7/77/10327a507.JPG page7]
 
−  [http://katlas.math.toronto.edu/drorbn/images/d/df/10327a508.JPG page8]
 
−  [http://katlas.math.toronto.edu/drorbn/images/9/9d/10327a509.JPG page9]
 
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−  [http://katlas.math.toronto.edu/drorbn/images/7/75/10327a511.JPG page11]
 
−  [http://katlas.math.toronto.edu/drorbn/images/7/70/10327a512.JPG page12]
 
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−  [http://katlas.math.toronto.edu/drorbn/images/c/c5/10327a515.JPG page15]
 
−  [http://katlas.math.toronto.edu/drorbn/images/6/6d/10327a516.JPG page16]
 
−  [http://katlas.math.toronto.edu/drorbn/images/c/c6/10327a517.JPG page17]
 
−  [http://katlas.math.toronto.edu/drorbn/images/d/d5/10327a518.JPG page18]
 
− 
 
−  An assignment without a solution is like a nightmare to me. I like every question accompanied
 
−  with a clean solution aside.(Might not be the case for research question because they are just
 
−  simply too hard.) I would like to share this happiness of understanding and acquiring knowledge
 
−  with everybody because I don't think this class is a battle. I certainly don't like the idea that
 
−  we should keep information/answers as something like business secrets. This learning process
 
−  should be enjoyable which should be full of discussions instead of things like "you have to think on
 
−  your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe
 
−  a positive learning environment is crucial to truly understanding something well although we should not neglect
 
−  independent thinking at the same time. That is why I share whatever I have with you. If I am wrong feel free to criticize
 
−  me, and I am pretty sure a lot of people don't agree with me. But that is OK because there is just no
 
−  absolute right or wrong and everybody is doing what they think is right. Just like you can't say if
 
−  Axiom of choice is right or not. If you believe then it is right. If you don't believe it then it is wrong.
 
−  Or maybe, for the entire subjectmath, if you believe it then it is right. If you don't believe it then it
 
−  is completely wrong.Kai
 
Latest revision as of 22:54, 10 December 2010
Additions to the MAT 327 web site no longer count towards good deed points

#

Week of...

Notes and Links

1

Sep 13

About This Class, Monday  Continuity and open sets, Thursday  topologies, continuity, bases.

2

Sep 20

Monday  More on bases, Thursdsay  Products, Subspaces, Closed sets, HW1, HW1 Solutions

3

Sep 27

Monday  the Cantor set, closures, Thursday, Class Photo, HW2, HW2 Solutions

4

Oct 4

Monday  the axiom of choice and infinite product spaces, Thursday  the box and the product topologies, metric spaces, HW3, HW3 Solutions

5

Oct 11

Monday is Thanksgiving. Thursday  metric spaces, sequencial closures, various products. Final exam's date announced on Friday.

6

Oct 18

Monday  connectedness in , HW4, HW4 Solutions, Thursday  connectedness, pathconnectedness and products

7

Oct 25

Monday  Compactness of , Term Test on Thursday, TT Solutions

8

Nov 1

Monday  compact is closed and bounded, maximal values, HW5, HW5 Solutions, Wednesday was the last date to drop this course, Thursday  compactness of products and in metric spaces, the FIP

9

Nov 8

MondayTuesday is Fall Break, Thursday  Tychonoff and a taste of StoneCech, HW6, HW6 Solutions

10

Nov 15

Monday  generalized limits, Thursday  Normal spaces and Urysohn's lemma, HW7, HW7 Solutions

11

Nov 22

Monday  and , Thursday  Tietze's theorem

12

Nov 29

Monday  compactness in metric spaces, HW8, HW8 Solutions, Thursday  completeness and compactness

13

Dec 6

Monday  Baire spaces and nowhere differentiable functions, Wednesday  Hilbert's 13th problem; also see December 2010 Schedule

R

Dec 13

See December 2010 Schedule

F

Dec 20

Final exam, Monday December 20, 2PM5PM, at BR200

Register of Good Deeds

Add your name / see who's in!

See Hilbert's 13th


Reading
Read sections 26 and 27 in Munkres' textbook (Topology, 2nd edition). Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read. Also, preread sections 28 and 29, just to get a feel for the future.
Doing
Solve the following problems from Munkres' book, though submit only the underlined ones: Problems 1, 4, 5, 6, 7, 8, 9, 12 on pages 170172, and problem 2 on page 177. (For the last, recall that ).
Due date
This assignment is due at the end of class on Thursday, November 11, 2010.

Dror's notes above / Student's notes below


 Question. In 4. By bounded metric space you mean there exists a point and an epsilon where this epsilon nbd contains everything in the metric space? Kai
 Indeed so, though usually when talking about boundedness, people use the letter and not the letter . It makes no difference, of course.