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cs.LO2021
The Point-to-Set Principle and the Dimensions of Hamel Bases
Jack H. Lutz, Renrui Qi, Liang Yu
We prove that every real number in [0,1] is the Hausdorff dimension of a Hamel basis of the vector space of reals over the field of rationals. The logic of our proof is of particul…
cs.LO2004
The Arithmetical Complexity of Dimension and Randomness
John M. Hitchcock, Jack H. Lutz, Sebastiaan A. Terwijn
Constructive dimension and constructive strong dimension are effectivizations of the Hausdorff and packing dimensions, respectively. Each infinite binary sequence A is assigned a d…