Scanning the structure of ill-known spaces: Part 2. Principles of   construction of physical space
  Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of reference in order to account for the successive positions of any objects present in the system. Mappings from one to the next section involve morphisms of the general structures. Discrete properties of the lattice allow the prediction of scales at which microscopic to cosmic structures should occur. Deformations of primary cells by exchange of empty set cells allow a cell to be mapped into an image cell in the next section as far as mapped cells remain homeomorphic. If a deformation involves a fractal transformation to objects, there occurs a change in the dimension of the cell and the homeomorphism is not conserved. The fractal kernel stands for a "particle" and the reduction of its volume is compensated by morphic changes of a finite number of surrounding cells. Quanta of distances and quanta of fractality are demonstrated. The interaction of a moving particle-like deformation with the surrounding lattice involves a fractal decomposition process that supports the existence and properties of previously postulated inerton clouds as associated to particles. Experimental evidence and further possibilities of the existence of inertons are proposed. 
Michel Bounias, Volodymyr Krasnoholovets