10-327/Classnotes for Thursday November 25

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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

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

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)

-Picture

One picture summary of what you should know about regular/completely regular/normal/completely normal spaces. -KaiXwbdsb 07:59, 19 December 2010 (EST) http://katlas.math.toronto.edu/drorbn/index.php?title=Image:10-327_review.JPG