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

Register of Good Deeds

Add your name / see who's in!

See Hilbert's 13th


Some blackboard shots are at BBS/10_327100930143624.jpg.

Dror's notes above / Student's notes below


Here are some lecture notes..
Lecture 6 page 1
Lecture 6 page 2
Lecture 6 page 3
Lecture 6 page 4
Lecture 6 page 5
D 12:48, 2 October 2010 (EDT) finite Hausdorff space: The only topology satisfying Hausdorff for a finite set A is the discrete topology; for each distinct point x and y in A, {x} and {y} are disjoint. Also, every finite point set in A is closed. We can check that using the discrete metric on A (d(x,y) = 1 if x =/= y, d(x,y) = 0 if x=y), a sequence of points in A can converge to only one point at most. Also note that Hausdorff condition is stronger than T1.
Discrete topology implies Hausdorrf condition is obvious. The converse we can prove by contradiction so that its much clearer. Suppose the space X is Hausdorff but it does not have discrete topology. So some finite subset A would not be open. A complement is a finite subset of X would not be closed. That cannot happen because Hausdorff condition implies T1 so that any finite union of singleton set should still be closed. Contradiction here. Kai Xwbdsb 13:31, 4 October 2010 (EDT)