We have F being a subset of R, [-1,1], while f:R->R, where f(x)=x^2. What's the Hausdorff dimension of F and f(F)? I think the dim(F)=2(length) and dim(f(F))=1, is it correct? Thanks,
2025-01-13 02:19:08.1736734748
Hausdorff dimension of F and f(F)
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Definitely not correct. Any interval (of any lenght) has Hausdorff dimension 1. The Cantor set has measure zero and Hausdorff dimension $\log_3(2)$.