Classical physics features plenty of paradoxes and unsolved problems. It is proved that sometimes the interpretation of results of a successful practical formalization of some phenomena has turned out to be a mistake; therefore, false physical representations of objects with nonexistent properties have been established in classical physics. Further analysis of such physical representations with the help of physical intuition has resulted in paradox, accordingly. The hypothesis involves alternative physical representations of objects that comply with the same mathematical equations. In particular, a physical representation of structural components of the matter (in this hypothesis referred to as space intervals) is used as the basis for forming the Space representation, which may be analyzed with the help of physical intuition and logic and allows to find valid answers to the problems related to its fundamental properties. The study proves that there is the Intranuclear Space along with familiar Macro Space, which drastically differ from each other. Specific properties of the Intranuclear Space have allowed to create conditions for forming more complicated objects that the Electron (Positron), Photon, and Neutrino. The hypothetic Macro Space has all fundamental properties with one amendment only – the principle of relativity is approximately fulfilled. However, due to small values of attractive forces in real processes, the violation of this principle is practically unnoticeable. The study contains some notes related to a number of objects and phenomena of the Global Space (dark matter, Einstein shift, the moment of the Universe's birth, black holes, proper time). This hypothesis offers one of possible variants of the Space structure. As the velocity of interstitial interaction is higher than the velocity of light while being not an infinite value, along this the fact that it passes in the structureless imaginary part of the complex Space, any theoretical studies in the field of General Theory of Relativity are becoming more urgent while the issue related to gravitational waves is still open. Keywords: Continuum, Universe expansion; closure, infinity and homogeneity of Space; principle of relativity, directivity of Time; Photon, particle Mass, space intervals.