About 20 years ago we published the data concerning some peculiarities of the behavior of cosmic radiation EAS hadron component spectra. The results pointed to the possible existence in the interstellar space of the background of weakly interacting objects of the mass (the energy of the resonance oscillations) of the order of 37 eV. The absence of such background particle creation in accelerator experiments may mean that it is not the elementary particle but the object of some different nature. On the other hand, the experimental data of the last years are pointing to the existence of cosmic gamma radiation with the specific spectrum having the steep right front again in the region of the order of 37 eV and the left front falling down to the energies of the order less than 10-6 eV. Obviously, no elementary object may possess such spectrum of frequencies or a decay spectrum. Such spectrum may have for example the topological defect of the space. Further the possibility will be presented of exactly such explanation of the cosmic rays primary radiation spectra peculiarities experimentally observed. It is based on the hypothesis about the discreteness of the space and existence in it of the topological defects distributed with sufficient density. In the frames of the proposed model some essential experimental peculiarities of the primary cosmic radiation nuclei and gamma quanta spectra find the unified explanation.