The Homeomorphism between the Logistics Space and the Information Space: The Criterion for Maximizing the Value of the Social Logistics System

Abstract

The principles to estimate the value of the social logistics system is based on the point of General System Theory, Cybernetics and Information Theory. The criterion of maximizing the value of a social logistics system is put forward which is the homeomorphism between the logistics space and the information space. The logistics space and the information space in the social economic system are defined by introducing the conception of topological space and group. The features and the relationships of the logistics space and information space were described respectively. It can be concluded that the key characteristic of the most optimized social logistics system is homeomorphism between the logistics space and the information space. On this basis, the method to describe the homeomorphism between two topological spaces by the isomorphism of two fundamental groups and the example of the supply system are represented further. 1. THE INFORMATION AND LOGISTICS SPACE WHICH CONDUCTED TO THE TOPOLOGICAL SPACE 1.1. Topological space and fundamental group The definition of the topological space: Let X to be any set and let T to be a family of subsets of X. Then T is a topology on X if (1) Both the empty set and X are elements of T. (2)Any union of arbitrarily many elements of T is an element of T. (3)Any intersection of finitely many elements of T is an element of T. If T is a topology on X, then the pair (X, T) is called a topological space (James 2006). The topological basis definition: if X is a set, a basis for a topology on X is a collection B of subsets of X (called basis elements) satisfying the following properties. (1)For each x∈X, there is at least one basis element B containing x. (2)If x belongs to the intersection of two basis elements B1 and B2, then there is a basis element B3 containing x such that . To state it another way, a topological basis is a subset B of a set T in which all other open sets can be written as unions or finite intersections of B. Homeomorphism and homotopy: A function f: X → Y between two topological spaces (X, TX) and (Y, TY) is called a homeomorphism if it has the following properties: (1)f is a bijection (one-to-one and onto), (2)f is continuous, (3)The inverse function f −1 is continuous (f is an open mapping). Formally, a homotopy between two continuous functions f and g from a topological space X to a topological space Y is defined to be a continuous function H : X × [0,1] → Y from the product of the space 2144 ICLEM 2010: Logistics for Sustained Economic Development © 2010 ASCE