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Before, I claimed that the Cantor set is homoeomorphic to the p-adic integers; now I'm not so sure and I played it safe and replaced "p-adic" by "2-adic". Does anybody know if the 3-adic's are homoeomorphic to our Cantor set? --AxelBoldt
Before, I claimed that the Cantor set is homoeomorphic to the p-adic integers; now I'm not so sure and I played it safe and replaced "p-adic" by "2-adic". Does anybody know if the 3-adic's are homoeomorphic to our Cantor set? --AxelBoldt

Yes. Every nonempty totally-disconnected perfect compact metric space is homeomorphic to the Cantor set. --Zundark, 2001 Nov 30
Before, I claimed that the Cantor set is homoeomorphic to the p-adic integers; now I'm not so sure and I played it safe and replaced "p-adic" by "2-adic". Does anybody know if the 3-adic's are homoeomorphic to our Cantor set? --AxelBoldt

Yes. Every nonempty totally-disconnected perfect compact metric space is homeomorphic to the Cantor set. --Zundark, 2001 Nov 30

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Last edited December 1, 2001 5:26 am by Zundark (diff)
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