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 ${\mathbb {R} }$, HW4, HW4 Solutions, Thursday  connectedness, pathconnectedness and products

7

Oct 25

Monday  Compactness of $[0,1]$, 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  $T_{3.5}$ and $I^{A}$, 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

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See Hilbert's 13th


In order to make our topological space of homework assignments complete, I need to upload the solution to the last assignment.(Sorry for getting so busy and keep forgetting things) What metric we should put on it?...Its quite difficult to create a complete space...
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Kai Xwbdsb 07:32, 19 December 2010 (EST)
I think the set of homeworks is a finite point set, hence automatically compact ... if you view the homeworks as spaces instead of points, then the resulting product space is complete if each homework is complete, as we know ... exercise: (a) is the converse also true? (b) what about infinite products?
The resulting product space is complete only if you put that weird metric that induces the product topology. When the space is not metric we cannot talk about completeness. Converse depends on what kind of metric you define on the projection? countable infinite product is done in the book. It is complete with that weird metric induced from metrics from all the spaces.Kai
Anyway, here is another solution set, this one typed (though not graded, so use at your own risk): Bcd 14:40, 19 December 2010 (EST)
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