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I set out to model a lattice version of a smooth space. A discretization procedure not uncommon in physics, but there's a catch: every connected point has the same distance. Which essentially breaks everything I knew about lattices. So I'm not putting points on a plane (where each point would have its own coordinates) but making a plane out of points. So each point only has has information about its connectivity with its surroundings. This is closer to graph theory, I believe.

This smells a lot like topology, that's why I came here. Is there a way to retrieve information, like number of dimensions, or even geometrical aspects like curvature, in some limit where this graph/lattice tends to a continuum space? This limit would be an increase in number of points or something like that.