作者cckk3333 (皓月)
看板Math
标题[分析] 两题
时间Tue Jan 18 22:43:47 2011
1. Let (M,d) be a metric space and f: M -> M satisfy
d(x,y) <= d(f(x),f(y))<= 2*d(x,y) for all x,y
Show that d(f(x),f(y)) = d(x,y) for all x,y and f is bijection
2. Let f: R -> R be a bounded function. Prove that f is continuous if and
only if the graph = { (x,y) | y = f(x) } of f is a closed subset of R^2
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1F：推 math1209 :1.题目没错? f:|R -> |R, f(x):= 2x. 01/18 22:58
2F：→ math1209 :2. Use the fact: Rudin, 高微, Thm 4.17. 01/18 23:00
3F：→ cckk3333 :1感觉一楼是对的 这是期末考题没有解答我也没把握 01/18 23:02
4F：推 math1209 :或许加上 M is compact. 01/18 23:05
5F：→ cckk3333 :有可能 不过我确定题目没有compact 01/18 23:07
6F：推 yusd24 :M 是 compact..期末考的时候有改题目 01/18 23:43
7F：推 thisday :(M,d) be a compact metric space 01/18 23:44
8F：推 thisday :疑! 楼上助教先回了!! 01/18 23:46
9F：推 yusd24 :楼上误会了 我不是高微助教.. 01/18 23:48
10F：推 thisday :推代导助教^^ 01/18 23:51
11F：→ cckk3333 :喔 抱歉我考试的时候太紧张没注意到 01/18 23:57
12F：→ cckk3333 :跟所有看这题的版友郑重道歉!! 01/18 23:58
13F：推 yusd24 :奇怪了...怎麽大家都知道我的 id o_O 01/19 00:00