Kinematic changeable sets with given universal coordinate transformation

Abstract

This work is devoted to the investigation of kinematic changeable sets (“abstract kinematics”), that is the mathematical objects, in which changeable sets are equipped by different geometrical or topological structures, namely metric, topological, linear, Banach, Hilbert and other spaces. Such mathematical objects allow to simulate the evolution of physical systems in a framework of different laws of kinematics. Existence of a few different kinematic theories of tachyon motion may serve as a physical motivation for investigations in this direction. In the paper the main properties of kinematic sets with given universal coordinate transform are investigated and examples of their application to mathematically strict foundation of tachyon kinematics are presented.