2011/08/30 by Enrico Le Donne, Donne, Enrico Le
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG
paper · pdf · doi:10.48550/arxiv.1108.5830
25 pages. Missing references of previous contributions added. Some credits and attributions corrected
openalex publication_date 2011/08/30 · arxiv created 2011/09/04 · arxiv updated 2011/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on \R that are translation invariant. We study possible values of various metric dimensions of such spaces. One of the main results is the equivalence of two properties: the first one is linear connectedness and the second one is 1-dimensionality, with respect to Nagata dimension. Several concrete pathological examples are provided.