|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 , 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 - and , 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_327-101206-142909.jpg.
||Dror's notes above / Student's notes below
- Question. The fact that the metric space of real-valued 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 non-compact 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)
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.