Additions to the MAT 327 web site no longer count towards good deed points

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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


See some blackboard shots at BBS/10_327101125142103.jpg.

Dror's notes above / Student's notes below


Here is a lecture note for today:
Lecture Nov 25
Question
Question. The first half of Tietze's theorem isn't very surprising as a limiting process of approximations.
But the second half is just like a magic? I don't understand what has been implicitly used here. The "boundedness"
property only depends on the metric we define on a set and it does not have anything to do with topology.
We are linking R with (1,1) with a homeomorphism which is completely not metricrelated. And suddenly all the unbounded
cts functions all become bounded cts functions?......What has been used here? Did we implicitly redefined the metric?
Why it works out so smoothly just like a magic trick?...
Kai
Kai  your question is too openended to have an answer that fits in a few minutes of typing, so I'd rather answer it in person, if you come to my office hours. Drorbn 16:39, 6 December 2010 (EST)
Picture
One picture summary of what you should know about regular/completely regular/normal/completely normal spaces. KaiXwbdsb 07:59, 19 December 2010 (EST)
http://katlas.math.toronto.edu/drorbn/index.php?title=Image:10327_review.JPG