Combining the mathematical general relativistic and quantum mechanical properties with the strong field interactions available in the systems is a powerful way of creating quantum dynamic space manipulation and functionalities. In chapter 1 it’s shown that this consequence creates mathematically difficulties for the General relativistic in Einstein theory of gravity, in it the presence of mass and energy warp the fabric of space and time. Chapter 2 will show that this implication creates difficulty for the Schwartz space. Chapter 3 deals with the Schrodinger equation, which tracks these probability waves through space and time. Chapter 4 deals with the right kind of function spaces for time-frequency analysis of consequences homogeneous and systematics space. The conclusion is reached that space can be formed as a result of the growth of perturbation that was initially small. The propagation and absorption of space are also investigated in this approximation. In chapter 5, quantum space in the consequences of quantum is examined by a method of asymptotic of General Relativity, Quantum Mechanics, Besov-type, and Feichtinger’s algebra. The ‘peeling-off’ behavior and the asymptotic group are derived. Chapter 6 deals with the occurrence of singularities in quantum space models. It is shown that singularity is inevitable provided that certain very general conditions are satisfied.