The Point-to-Set Principle and the dimensions of Hamel bases-Reference-Cited by-同舟云学术

The Point-to-Set Principle and the dimensions of Hamel bases

Published:2024-02-05 Issue: Volume: Page:1-8
ISSN:2211-3576
Container-title:Computability
language:
Short-container-title:COM

Author:

Lutz Jack H.¹,Qi Renrui²,Yu Liang³

Affiliation:

1. Department of Computer Science, Iowa State University, Ames, IA 50011, USA

2. School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand

3. Department of Mathematics, Nanjing University, Jiangsu Province 210093, P.R. of China

Abstract

We prove that, for every 0 ⩽ s ⩽ 1, there is a Hamel basis of the vector space of reals over the field of rationals that has Hausdorff dimension s. 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).

Publisher

IOS Press

Subject

Artificial Intelligence,Computational Theory and Mathematics,Computer Science Applications,Theoretical Computer Science

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