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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 [math]\displaystyle{ {\mathbb R} }[/math], 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 [math]\displaystyle{ [0,1] }[/math], 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 - [math]\displaystyle{ T_{3.5} }[/math] and [math]\displaystyle{ I^A }[/math], 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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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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Reading
Read sections [math]\displaystyle{ \{31,32,33\} }[/math] 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 [math]\displaystyle{ \emptyset }[/math], just to get a feel for the future.
Doing
Solve and submit the following problems from Munkres' book:
- Problem 1 on page 199.
- Problem 1 on page 205.
- Problems 1, 4, 5, 8, 9 on pages 212-213.
Remark. The following fact, which we will prove later, may be used without a proof: If [math]\displaystyle{ X }[/math] is a topological space and [math]\displaystyle{ f_n:X\to[0,1] }[/math] are continuous functions, then the sum [math]\displaystyle{ f(x):=\sum_{n=1}^\infty\frac{f_n(x)}{2^n} }[/math] is convergent and defines a continuous function on [math]\displaystyle{ X }[/math].
Due date
This assignment is due at the end of class on Thursday, November 25, 2010.
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Dror's notes above / Student's notes below
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- Question: In problem 1 p205, is asks us to show that any closed subspace of a normal space is also normal. Do we really need the condition that the subspace be closed? - Jdw
- Yes. Drorbn 19:14, 19 November 2010 (EST)
Questions by Kai Xwbdsb 21:26, 19 November 2010 (EST) were moved to Classnotes for Thursday November 18 as they are about that class and not about this assignment. Drorbn 06:03, 20 November 2010 (EST)
