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 , HW4, HW4 Solutions, Thursday  connectedness, pathconnectedness and products

7

Oct 25

Monday  Compactness of , 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  and , 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


See some blackboard shots at BBS/10_327101206142909.jpg.
Video: Topology101206

Dror's notes above / Student's notes below


Lecture Notes
 Question. The fact that the metric space of realvalued functions on the unit interval with uniform metric is complete uses the fact that [0,1] is compact right? If the function space is defined on a noncompact topological space is that necessarily complete?... Kai Xwbdsb 00:01, 20 December 2010 (EST)
 No, the compactness of is not used. As we said in class, if is Cauchy in the uniform metric, then for any , the sequence is Cauchy in , so it has a limit. Call that limit ; it is not hard to show that is continuous and that . Theorem 43.6 in Munkres is a slight generalization of this. Drorbn 07:12, 20 December 2010 (EST)
Thanks Dror.
Everybody good luck on the exam!Kai
Great course! Thank you very much for all your help Dror and all the classmates in this class.
Kai