Research On Connectivity Of Posets

This thesis mainly studies the connectivity of.There are two mainly aspects.First,the definition and properties of connectivity are given on a finite posets.Second,the concept of connectivity is defined on a posets and some properties of connectivity are given.In fact,the latter is the generalization of the former.So we first investigate the step sets,and use step sets as tools to establish an connected relation between elements on the(finite)posets.In addition,the concepts of branche,separable branche and unseparable branche are given on the(finite)disjoint-posets.It is pointed out that the real connected set,the unconnected poset and disjoint-posets can be infer each other in structure.Finally,we discuss the unity of connectivity between the finite posets and the posets.The main research work of this paper is as follows:1.In the third chapter,we construct the concept of step sets,get the fixed setseries.And explore the fixed set-series,give some good results.Make a good paving for the definition of the connectivity on the(finite)posets.2.In the fourth chapter,because arbitrary element of a finite posets produce a fixed set-series.So it can be used as the definition of connectivity between the elements with the maximum step sets equal.And some properties about the connected branch are obtained.3.In the fifth chapter,the finite condition is removed.The connectivity properties on the posets are discussed.Using the step sets as a tool to define the concept of connectivity.The relationship among real connected set,the unconnected poset,and the disjoint posets are studied.4.In the sixth chapter,we mainly explore the compatibility of connectivity between poset and finite poset.