|Additions to the MAT 327 web site no longer count towards good deed points
||Notes and Links
||About This Class, Monday - Continuity and open sets, Thursday - topologies, continuity, bases.
||Monday - More on bases, Thursdsay - Products, Subspaces, Closed sets, HW1, HW1 Solutions
||Monday - the Cantor set, closures, Thursday, Class Photo, HW2, HW2 Solutions
||Monday - the axiom of choice and infinite product spaces, Thursday - the box and the product topologies, metric spaces, HW3, HW3 Solutions
||Monday is Thanksgiving. Thursday - metric spaces, sequencial closures, various products. Final exam's date announced on Friday.
||Monday - connectedness in , HW4, HW4 Solutions, Thursday - connectedness, path-connectedness and products
||Monday - Compactness of [0,1], Term Test on Thursday, TT Solutions
||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
||Monday-Tuesday is Fall Break, Thursday - Tychonoff and a taste of Stone-Cech, HW6, HW6 Solutions
||Monday - generalized limits, Thursday - Normal spaces and Urysohn's lemma, HW7, HW7 Solutions
||Monday - T3.5 and IA, Thursday - Tietze's theorem
||Monday - compactness in metric spaces, HW8, HW8 Solutions, Thursday - completeness and compactness
||Monday - Baire spaces and no-where differentiable functions, Wednesday - Hilbert's 13th problem; also see December 2010 Schedule
||See December 2010 Schedule
||Final exam, Monday December 20, 2PM-5PM, at BR200
|Register of Good Deeds
Add your name / see who's in!
See Hilbert's 13th
See some blackboard shots at BBS/10_327-101125-142103.jpg.
||Dror's notes above / Student's notes below
Here is a lecture note for today:
Lecture Nov 25
Question. The first half of Tietze's theorem isn't very surprising as a limiting process of approximations.
But the second half is just like a magic? I don't understand what has been implicitly used here. The "boundedness"
property only depends on the metric we define on a set and it does not have anything to do with topology.
We are linking R with (-1,1) with a homeomorphism which is completely not metric-related. And suddenly all the unbounded
cts functions all become bounded cts functions?......What has been used here? Did we implicitly redefined the metric?
Why it works out so smoothly just like a magic trick?...
Kai - your question is too open-ended to have an answer that fits in a few minutes of typing, so I'd rather answer it in person, if you come to my office hours. Drorbn 16:39, 6 December 2010 (EST)
One picture summary of what you should know about regular/completely regular/normal/completely normal spaces. -KaiXwbdsb 07:59, 19 December 2010 (EST)