二元关系传递性泛系研究新探

A New Pansystems Research About Binary Relation's Transitivity

本文基于泛系数学研究和一般事物机理分析的需要，讨论了二元关系对多元关系的传递性，引进一种被叫作“ｇ－传递性”的广义传递概念，考察了它的基本性质，ｇ－传递性不但是普通传递性、拟传递性、半序、拟半序等泛序概念的推广，还包容闭性、凸性、拓扑、对偶性等基本概念为其特例，从而表明这一概念的普适性。

Because of the great needs for both the research of pansystems mathematics and the analysis of general things’mechanism,this paper discusses the binary relation's transitivity confined to multirelation. The so-called “g-transi-tivity”a completely new eoncept about transitivity-is introduced and its basic properties are investigated.The study shows that it is not only g-transiti-vity a generalization of traditional transitivity,quasi-transitivity, semi-order, quasi-order and other panorder,but also includes many basic concepts such as closeness,convexity,topology,duality as its special cases.