[分析] 兩題

[cckk3333 (皓月)]

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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推 math1209    :1.題目沒錯? f:|R -> |R, f(x):= 2x.
→ math1209    :2. Use the fact: Rudin, 高微, Thm 4.17.
→ cckk3333    :1感覺一樓是對的 這是期末考題沒有解答我也沒把握
推 math1209    :或許加上 M is compact.
→ cckk3333    :有可能 不過我確定題目沒有compact
推 yusd24      :M 是 compact..期末考的時候有改題目
推 thisday     :(M,d) be a compact metric space
推 thisday     :疑! 樓上助教先回了!!
推 yusd24      :樓上誤會了  我不是高微助教..
推 thisday     :推代導助教^^
→ cckk3333    :喔 抱歉我考試的時候太緊張沒注意到
→ cckk3333    :跟所有看這題的版友鄭重道歉!!
推 yusd24      :奇怪了...怎麼大家都知道我的 id o_O