128200 20241125101159.0 doi 10.1016/j.ic.2023.105078 sideral 135357 ART-2023-135357 eng Lutz, Jack H. Extending the reach of the point-to-set principle 2023 Access copy available to the general public Unrestricted The point-to-set principle of J. Lutz and N. Lutz (2018) has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces [Rn]. These are classical questions, meaning that their statements do not involve computation or related aspects of logic. In this paper we extend the reach of the point-to-set principle from Euclidean spaces to arbitrary separable metric spaces X. We first extend two algorithmic dimensions—computability-theoretic versions of classical Hausdorff and packing dimensions that assign dimensions [dim(x)] and [Dim(x)] to individual points [x E X] —to arbitrary separable metric spaces and to arbitrary gauge families. Our first two main results then extend the point-to-set principle to arbitrary separable metric spaces and to a large class of gauge families. We demonstrate the power of our extended point-to-set principle by using it to prove new theorems about classical fractal dimensions in hyperspaces. info:eu-repo/grantAgreement/ES/DGA/T64-20R info:eu-repo/grantAgreement/ES/MICINN/PID2022-138703OB-I00 info:eu-repo/grantAgreement/ES/MINECO/PID2019-104358RB-I00 info:eu-repo/grantAgreement/ES/MINECO/TIN2016-80347-R info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 0.8 2023 MATHEMATICS, APPLIED 219 / 332 = 0.66 2023 Q3 T2 COMPUTER SCIENCE, THEORY & METHODS 102 / 144 = 0.708 2023 Q3 T3 0.57 2023 Computational Theory and Mathematics 2023 Q2 Computer Science Applications 2023 Q2 Information Systems 2023 Q2 Theoretical Computer Science 2023 Q3 2.3 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Lutz, Neil Mayordomo, Elvira Universidad de Zaragoza (orcid)0000-0002-9109-5337 5007 570 Universidad de Zaragoza Dpto. Informát.Ingenie.Sistms. Área Lenguajes y Sistemas Inf. 294 (2023), 105078 [19 pp.] Inf. comput. INFORMATION AND COMPUTATION 0890-5401 480548 http://zaguan.unizar.es/record/128200/files/texto_completo.pdf Versión publicada 2042030 http://zaguan.unizar.es/record/128200/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:128200 articulos driver 2024-11-22-12:11:00 ARTICLE