Register to reply

Set of p-adic integers is homeomorphic to Cantor set; how?

by benorin
Tags: cantor, homeomorphic, integers, padic
Share this thread:
benorin
#1
Nov27-05, 11:34 AM
HW Helper
P: 1,025
Could somebody explain with due brevity why/how the set of p-adic 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 p-adic integers, and, if one point is removed from it, to the p-adic numbers."

Can somebody explain this simply, I don'y really get p-adic #'s.

P.S. Not homework, don't want a proof, just understanding of it.
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
matt grime
#2
Nov27-05, 11:39 AM
Sci Advisor
HW Helper
P: 9,396
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 2-adics (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.


Register to reply

Related Discussions
Is Q Homeomorphic to N? Calculus 3
P-adic sequence Calculus & Beyond Homework 1
P-adic metric Calculus & Beyond Homework 0
P-adic convergence Introductory Physics Homework 5
P-adic number Linear & Abstract Algebra 0