Sunday, January 24, 2016

functions - Bijection from [0,1]3 to [0,1]?





Is there any bijection from [0,1]3 to [0,1]? How can I construct it?


Answer



Hint:



If there exists a surjection between A to B and a surjection between B to A, then there exists a bijection between A to B. In your case, space filling curves are surjections from [0,1] to [0,1]3. It should be easy to find a surjection going the other way.


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