  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.
