Extending the reach of the point-to-set principle

Lutz, Jack H. ; Lutz, Neil ; Mayordomo, Elvira (Universidad de Zaragoza)

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.ic.2023.105078

Año: 2023

Publicado en: INFORMATION AND COMPUTATION 294 (2023), 105078 [19 pp.]
ISSN: 0890-5401

Factor impacto JCR: 0.8 (2023)

Categ. JCR: MATHEMATICS, APPLIED rank: 218 / 331 = 0.659 (2023) - Q3 - T2
Categ. JCR: COMPUTER SCIENCE, THEORY & METHODS rank: 102 / 143 = 0.713 (2023) - Q3 - T3

Factor impacto CITESCORE: 2.3 - Information Systems (Q3) - Theoretical Computer Science (Q3) - Computational Theory and Mathematics (Q3) - Computer Science Applications (Q3)

Factor impacto SCIMAGO: 0.57 - Computational Theory and Mathematics (Q2) - Computer Science Applications (Q2) - Information Systems (Q2) - Theoretical Computer Science (Q3)

Financiación: info:eu-repo/grantAgreement/ES/DGA/T64-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2022-138703OB-I00
Financiación: info:eu-repo/grantAgreement/ES/MINECO/PID2019-104358RB-I00
Financiación: info:eu-repo/grantAgreement/ES/MINECO/TIN2016-80347-R

Tipo y forma: Article (Published version)

Área (Departamento): Área Lenguajes y Sistemas Inf. (Dpto. Informát.Ingenie.Sistms.)