Topological complexes in analysis and design of large scale system-factorization methodology

Abstract

Large-scale management information systems, knowledge-based systems, neural systems, control systems and others are becoming extremely sophisticated. In order to investigate their hierarchical structure the author considers such systems as topological spaces. These systems are partitioned into numerous subsystems, cells or elements in the process of their analysis and design. Such decomposition is equivalent to representation of the corresponding topological space as a disjoint union of cells. A topological cell complex of some space X is built as a quotient space of X, which is constructed by representation of each cell as one point. Thus cell complexes and CW-complexes of topological spaces are considered as topological spaces with quotient topology. Such topological complexes contain fewer points than corresponding spaces, and preserve their structure. This feature makes them useful for structural systems analysis and design.<>