The three boundedness classes of homeomorphism groups of countable Stone spaces are exactly the coarse equivalence classes, with the middle class quasi-isometric to the Hamming cube and infinite Hamming graphs bi-Lipschitz equivalent.
A remark on Cantor derivative
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abstract
It is shown that, modulo an equivalence relation induced by finite correspondences preserving Cantor rank, the class of topological spaces is an integral semi-ring on which the Cantor derivative is precisely a derivation.
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2026 1verdicts
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Coarse geometry of homeomorphism groups: Classifying countable Stone spaces
The three boundedness classes of homeomorphism groups of countable Stone spaces are exactly the coarse equivalence classes, with the middle class quasi-isometric to the Hamming cube and infinite Hamming graphs bi-Lipschitz equivalent.