I am afraid this isnt correct. The spacetime in QFT is also described by a manifold, usually plane and with a lorentzian metric. So in both cases the description of the spacetime is made with the same mathematical structure: a manifold. Anyway, a manifold is also a topological space, which is nothing but a set with a topology defined on it, so in this sense a manifold is a set of "discrete" points (although not countable) labelled locally with his coordinates in a chart and being the points the elements of the set. Of coruse, you have to add other mathematical structures to this set to obtain a manifold.
Changing the subject, do you realize what are you doing? You are taking the data that fits on your crazy idea and ignoring the rest of data that doesnt.