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A generic method for combinatorial constructions of intrinsic geometricalspaces is presented. It is based on the well known inverse sequences of finitegraphs that determine (in the limit) topological spaces. If a pattern of theconstruction is sufficiently regular and uniform, then the notions of metric,geodesic and curvature can be defined in the space as the limits of theirfinite versions in the graphs. This gives rise to consider the graphs withmetrics as finite approximations of the geometry of the space. On the basis ofsimple and generic examples, several nonstandard and novel notions are proposedfor the Foundations of Geometry. They may be considered as a subject of acritical discussion.

Combinatorial constructions of intrinsic geometries