Re: [分析] Is there a continuous ONTO function?

[math1209 (ww)]

※ 引述《Rapiers (*.*)》之銘言：
: f is a continuous function, and f: Q --> R-Q, where Q is rational numbers.
: Can f be a "onto" function?
: 請高手給一點提示
: 被這個看似簡單的題目困住好久了..

  經典題目應該是這個：（不然你題目跟連續會一點關系都沒有)

  Is there a continuous function from |R into |R which mpas the irrational
  numbers into rational numbers and maps rational numbers into irrational
  numbers ?

  Ans: NO, by IVT (＜＝＞連續必將連通集合送至連通集合）.

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