Real physical space, as a purely mathematical structure built according tothe rules of set theory, topology, and fractal geometry, was proposed by MichelBounias (1943-2003) and the author. It emerges as a mathematical lattice ofprimary topological balls, which was named a tessellattice, and the size of acell/ball in the tessellattice is comparative with the Planck length, ∼ 10^{−35} m.Discrete fractal properties of the lattice allow the prediction of scales at whichsubmicroscopic to cosmic structures should occur. This approach allows thedevelopment of a submicroscopic concept of physics, which describes Natureat a much deeper level than offered by the quantum-mechanical formalismdeveloped at the atom scale, ∼ 10^{−10} m. In addition, the approach makesit possible to define such fundamental physical notions as mass and chargefrom first submicroscopic principles, and this actually means that fundamentalmathematics lays down the basic concepts of physics.