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- W4293765705 abstract "A separable metric space X is an H-null set if any uniformly continuous image of X has Hausdorff dimension zero. upper H-null, directed P-null and P-null sets are defined likewise, with other fractal dimensions in place of Hausdorff dimension. We investigate these sets and show that in 2^omega{} they coincide, respectively, with strongly null, meager-additive, T' and null-additive sets. Some consequences: A subset of 2^omega{} is meager-additive if and only if it is E-additive; if f:2^omega->2^omega{} is continuous and X is meager-additive, then so is f(X), and likewise for null-additive and T'-sets." @default.
- W4293765705 created "2022-08-31" @default.
- W4293765705 creator A5010207246 @default.
- W4293765705 date "2012-08-27" @default.
- W4293765705 modified "2023-09-26" @default.
- W4293765705 title "Small sets of reals through the prism of fractal dimensions" @default.
- W4293765705 doi "https://doi.org/10.48550/arxiv.1208.5521" @default.
- W4293765705 hasPublicationYear "2012" @default.
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