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by Sharlin 1688 days ago
> Considered as a topological space, Cantor space happens to have the same structure as the Cantor set […]

And this is, intuitively, because every element of the (standard) Cantor set can be expressed as a trinary number in the range [0, 1) where every digit is either 0 or 2 (because at every level the middle third is excluded in the construction of the set). That is, a string of exactly two symbols – that is, a bitstring.

1 comments

(Late edit: [0, 1] of course rather than [0, 1) since famously 0.222…_3 = 1!)