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Re: Onto [0,1]
Posted:
Apr 25, 2013 3:18 AM


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?



