2019/04/10 by Stanisław Ambroszkiewicz, Ambroszkiewicz, Stanislaw
Computer Science · Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Computational Geometry (cs.CG) #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Computer and information sciences #FOS: Mathematics #Mathematics and Applications #cs.CG #math.DG
paper · pdf · doi:10.48550/arxiv.1904.05173
openalex publication_date 2019/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the construction is sufficiently regular and uniform, then the notions of metric, geodesic and curvature can be defined in the space as the limits of their finite versions in the graphs. This gives rise to consider the graphs with metrics as finite approximations of the geometry of the space. On the basis of simple and generic examples, several nonstandard and novel notions are proposed for the Foundations of Geometry. They may be considered as a subject of a critical discussion.