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The Point-to-Set Principle and the Dimensions of Hamel Bases by Lutz, Jack H.; Qi, Renrui; Yu, Liang is a scholarly article available to read on EtoBox.

What is The Point-to-Set Principle and the Dimensions of Hamel Bases about?

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 particular interest. The statement of our theorem is classical; it does not involve the theory of computing. However, our proof makes essential use of algorithmic fractal dimension--a computability-theoretic construct--and the point-to-set principle of J. Lutz and N. Lutz (2018).

Author

Lutz, Jack H.; Qi, Renrui; Yu, Liang

Published

2021

Language

EN