Axiomatization of Motion in Virtual Topological Spaces

The goal of this paper is to survey problems of axiomatization in general, to survey of axiomatization of motion in various spaces and to present a system of axioms to present controlled motion of stretched objects with bounded velocity. Survey of peculiarities of axiomatization in mathematics based on works by A.A. Borubaev and G.M. Kenenbaeva, axiomatization of kinematical spaces is presented in the paper. A new notion of generalized kinematical space is defined: given a family of connected sets of a kinematical space (passes) and a family of connected (isomorphic) sets (things); “passes” contain continuous sequences of “objects”.