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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. |
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− | ===Solution===
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− | [http://katlas.math.toronto.edu/drorbn/images/7/77/10-327a501.JPG page1]
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− | An assignment without a solution is like a nightmare to me. I like every question accompanied
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− | with a clean solution beside.(Might not be the case for research question because they are just
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− | simply too hard.) I would like to share this happiness of understanding and acquiring knowledge
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− | with everybody because I don't think this class is a battle. I certainly don't like the idea that
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− | we should keep information/answers as something like business secretes. This learning process
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− | should be enjoyable which should be full of discussions instead of things like "you have to think on
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− | your own/ I can't tell you the answer". I know maybe other people might not agree with me but I believe
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− | a positive learning environment is crucial to truly learn something well although we should not neglect
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− | independent thinking. That is why I share whatever I have with you. If I am wrong feel free to criticize
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− | me, and I am pretty sure a lot of people don't agree with me. But that is OK because there is just no
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− | absolute right or wrong and everybody is doing what they think is right. Just like you can't say if
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− | Axiom of choice is right or not. If you believe then it is right. If you don't believe it then it is wrong.
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− | Or maybe, for the entire subject--math, if you believe it then it is right. If you don't believe it then it
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− | is completely wrong.-Kai
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Additions to the MAT 327 web site no longer count towards good deed points
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#
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Week of...
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Notes and Links
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1
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Sep 13
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About This Class, Monday - Continuity and open sets, Thursday - topologies, continuity, bases.
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2
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Sep 20
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Monday - More on bases, Thursdsay - Products, Subspaces, Closed sets, HW1, HW1 Solutions
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3
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Sep 27
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Monday - the Cantor set, closures, Thursday, Class Photo, HW2, HW2 Solutions
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4
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Oct 4
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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
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Oct 11
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Monday is Thanksgiving. Thursday - metric spaces, sequencial closures, various products. Final exam's date announced on Friday.
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6
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Oct 18
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Monday - connectedness in , HW4, HW4 Solutions, Thursday - connectedness, path-connectedness and products
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7
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Oct 25
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Monday - Compactness of , Term Test on Thursday, TT Solutions
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8
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Nov 1
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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
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Nov 8
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Monday-Tuesday is Fall Break, Thursday - Tychonoff and a taste of Stone-Cech, HW6, HW6 Solutions
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10
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Nov 15
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Monday - generalized limits, Thursday - Normal spaces and Urysohn's lemma, HW7, HW7 Solutions
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11
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Nov 22
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Monday - and , Thursday - Tietze's theorem
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12
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Nov 29
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Monday - compactness in metric spaces, HW8, HW8 Solutions, Thursday - completeness and compactness
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13
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Dec 6
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Monday - Baire spaces and no-where differentiable functions, Wednesday - Hilbert's 13th problem; also see December 2010 Schedule
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R
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Dec 13
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See December 2010 Schedule
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F
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Dec 20
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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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This assignment is due at the end of class on Thursday, November 11, 2010.