set of padic integers is homeomorphic to Cantor set; how?by benorin Tags: cantor, homeomorphic, integers, padic 

#1
Nov2705, 11:34 AM

HW Helper
P: 1,007

Could somebody explain with due brevity why/how the set of padic integers is homeomorphic to the Cantor set less one point for any prime p?
This is a quote from Wikipedia:Cantor Set: "The Cantor set is also homeomorphic to the padic integers, and, if one point is removed from it, to the padic numbers." Can somebody explain this simply, I don'y really get padic #'s. P.S. Not homework, don't want a proof, just understanding of it. 



#2
Nov2705, 11:39 AM

Sci Advisor
HW Helper
P: 9,398

Write down the bijection from the traditional representation of the cantor set as the reals in [0,1] with no 1's in the base three expansion to the 2adics (write backwards and put 1s instead of 2s at all points), it is not a deep topological property we're talking about, just a formal one, a little like the integers with the discrete topology are homeomorphic to the positive integers with the discrete topology.



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