doi:10.1016/j.ic.2023.105078engLutz, Jack H.Lutz, NeilMayordomo, ElviraExtending the reach of the point-to-set principleART-2023-135357The 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.2023http://zaguan.unizar.es/record/12820010.1016/j.ic.2023.105078http://zaguan.unizar.es/record/128200oai:zaguan.unizar.es:128200info:eu-repo/grantAgreement/ES/DGA/T64-20Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2022-138703OB-I00info:eu-repo/grantAgreement/ES/MINECO/PID2019-104358RB-I00info:eu-repo/grantAgreement/ES/MINECO/TIN2016-80347-RINFORMATION AND COMPUTATION 294 (2023), 105078 [19 pp.]by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess