Scanning the structure of ill-known spaces: Part 3. Distribution of topological structures at elemen- tary and cosmic scales

The distribution of the deformations of elementary cells is studied in an abstract lattice constructed from the existence of the empty set. One combination rule determining oriented sequences with continuity of set-distance function in such spaces provides a particular kind of spacetime-like structure that favors the aggregation of such deformations into fractal forms standing for massive objects. A correlative dilatation of space appears outside the aggregates. At the large scale, this dilatation results in an apparent expansion, while at the submicroscopic scale the families of fractal deformations give raise to families of particle-like structure. The theory predicts the existence of classes of spin, charges and magnetic properties, while quantum properties associated to mass have previously been shown to determine the inert mass and the gravitational effects. When applied to our observable spacetime, the model would provide the justifications for the existence of the creation of mass in a specified kind of ”void”, and the fractal properties of the embedding lattice extend the phenomenon to formal justifications of Big-Bang-like events without need for any supply of an extemporaneous energy.