000128200 001__ 128200 000128200 005__ 20240731103415.0 000128200 0247_ $$2doi$$a10.1016/j.ic.2023.105078 000128200 0248_ $$2sideral$$a135357 000128200 037__ $$aART-2023-135357 000128200 041__ $$aeng 000128200 100__ $$aLutz, Jack H. 000128200 245__ $$aExtending the reach of the point-to-set principle 000128200 260__ $$c2023 000128200 5060_ $$aAccess copy available to the general public$$fUnrestricted 000128200 5203_ $$aThe 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. 000128200 536__ $$9info:eu-repo/grantAgreement/ES/DGA/T64-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-138703OB-I00$$9info:eu-repo/grantAgreement/ES/MINECO/PID2019-104358RB-I00$$9info:eu-repo/grantAgreement/ES/MINECO/TIN2016-80347-R 000128200 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000128200 590__ $$a0.8$$b2023 000128200 592__ $$a0.57$$b2023 000128200 591__ $$aMATHEMATICS, APPLIED$$b218 / 331 = 0.659$$c2023$$dQ3$$eT2 000128200 593__ $$aComputational Theory and Mathematics$$c2023$$dQ2 000128200 591__ $$aCOMPUTER SCIENCE, THEORY & METHODS$$b102 / 143 = 0.713$$c2023$$dQ3$$eT3 000128200 593__ $$aComputer Science Applications$$c2023$$dQ2 000128200 593__ $$aInformation Systems$$c2023$$dQ2 000128200 593__ $$aTheoretical Computer Science$$c2023$$dQ3 000128200 594__ $$a2.3$$b2023 000128200 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000128200 700__ $$aLutz, Neil 000128200 700__ $$0(orcid)0000-0002-9109-5337$$aMayordomo, Elvira$$uUniversidad de Zaragoza 000128200 7102_ $$15007$$2570$$aUniversidad de Zaragoza$$bDpto. Informát.Ingenie.Sistms.$$cÁrea Lenguajes y Sistemas Inf. 000128200 773__ $$g294 (2023), 105078 [19 pp.]$$pInf. comput.$$tINFORMATION AND COMPUTATION$$x0890-5401 000128200 8564_ $$s480548$$uhttps://zaguan.unizar.es/record/128200/files/texto_completo.pdf$$yVersión publicada 000128200 8564_ $$s2042030$$uhttps://zaguan.unizar.es/record/128200/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000128200 909CO $$ooai:zaguan.unizar.es:128200$$particulos$$pdriver 000128200 951__ $$a2024-07-31-10:06:14 000128200 980__ $$aARTICLE