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Topic: Onto [0,1]
Replies: 40   Last Post: Apr 29, 2013 10:16 PM

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William Elliot

Posts: 1,440
Registered: 1/8/12
Re: Onto [0,1]
Posted: Apr 25, 2013 3:18 AM
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On Sun, 21 Apr 2013, baclesback@gmail.com wrote:

> More specifically, use the representation of x in C Cantor set in base 3
> with only 0's and 2's in the expansion of 3, and map
>
> f: x=0.a1a2..... ---> 0.b1b2.......
>
> Wheref(bi)= 0 , if ai=0 , f(bi)=1 , if ai=2 .
>
> This f is continuous, but not absolutely continuous ( which
> preserves sets of measure zero. )


Why is f continuous?



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