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- W2765757795 abstract "For metric spaces, the doubling property, the uniform disconnectedness, and the uniform perfectness are known as quasi-symmetric invariant properties. The David-Semmes uniformization theorem states that if a compact metric space satisfies all the three properties, then it is quasi-symmetrically equivalent to the middle-third Cantor set. We say that a Cantor metric space is standard if it satisfies all the three properties; otherwise, it is exotic. In this paper, we conclude that for each of exotic types the class of all the conformal gauges of Cantor metric spaces has continuum cardinality. As a byproduct of our study, we state that there exists a Cantor metric space with prescribed Hausdorff dimension and Assouad dimension." @default.
- W2765757795 created "2017-11-10" @default.
- W2765757795 creator A5072870097 @default.
- W2765757795 date "2017-10-23" @default.
- W2765757795 modified "2023-09-23" @default.
- W2765757795 title "Quasi-symmetric invariant properties of Cantor metric spaces" @default.
- W2765757795 doi "https://doi.org/10.48550/arxiv.1710.08190" @default.
- W2765757795 hasPublicationYear "2017" @default.
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