From Drorbn
| Additions to the MAT 327 web site no longer count towards good deed points
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| Week of...
| Notes and Links
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| 1
| Sep 13
| About This Class, Monday - Continuity and open sets, Thursday - topologies, continuity, bases.
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| 2
| Sep 20
| Monday - More on bases, Thursdsay - Products, Subspaces, Closed sets, HW1, HW1 Solutions
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| 3
| Sep 27
| Monday - the Cantor set, closures, Thursday, Class Photo, HW2, HW2 Solutions
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| 4
| Oct 4
| Monday - the axiom of choice and infinite product spaces, Thursday - the box and the product topologies, metric spaces, HW3, HW3 Solutions
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| 5
| Oct 11
| Monday is Thanksgiving. Thursday - metric spaces, sequencial closures, various products. Final exam's date announced on Friday.
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| 6
| Oct 18
| Monday - connectedness in  , HW4, HW4 Solutions, Thursday - connectedness, path-connectedness and products
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| 7
| Oct 25
| Monday - Compactness of [0,1], Term Test on Thursday, TT Solutions
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| 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
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| 9
| Nov 8
| Monday-Tuesday is Fall Break, Thursday - Tychonoff and a taste of Stone-Cech, HW6, HW6 Solutions
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| 10
| Nov 15
| Monday - generalized limits, Thursday - Normal spaces and Urysohn's lemma, HW7, HW7 Solutions
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| 11
| Nov 22
| Monday - T3.5 and IA, Thursday - Tietze's theorem
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| 12
| Nov 29
| Monday - compactness in metric spaces, HW8, HW8 Solutions, Thursday - completeness and compactness
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| 13
| Dec 6
| Monday - Baire spaces and no-where differentiable functions, Wednesday - Hilbert's 13th problem; also see December 2010 Schedule
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| R
| Dec 13
| See December 2010 Schedule
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| F
| Dec 20
| Final exam, Monday December 20, 2PM-5PM, at BR200
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| Register of Good Deeds
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Add your name / see who's in!
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See Hilbert's 13th
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See some blackboard shots at BBS/10_327-101125-142103.jpg.
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| Dror's notes above / Student's notes below
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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 metric-related. 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 open-ended 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:10-327_review.JPG
