DEFINITION OF GENERALIZED KINEMATICAL SPACES BY MEANS OF CONNECTED SETS

Abstract

          In the paper kinematical spaces with possibility of inner motion of stretched sets are investigated. The aim of the paper is to define large classes of such spaces by the axiomatic way. The method of axiomatic definition of natural motion of connected sets in the space is used. A system of axioms of spaces called generalized kinematical ones is built; it enlarges  the  well-known axiomatic  system for  kinematical topological spaces. The result obtained is a development of the general theory of virtual topological spaces with computer-implemented controlled natural motion of objects being created in Kyrgyzstan. This result can be used to build a soft yielding capacity of effective search and detecting dimension of virtual spaces. In the future, it is planned to create a general theory with practical implementation of motion, constructing and searching of objects and detecting of properties of virtual spaces having practical applications.