Some Problems Study In L-Pretopological Spaces

L-pretopological space is one generalization of L-topological space,it is more general than L-topological space and has some good properties.In this paper,some basis concepts(such asδ-subset,δ-continuous order homorphism) of L-pretopological space are introduced and its some basic propertities are discussed,thenδ-convergences,δ-connectedness,δ-component and localδ-connectedness are mainly investigated in L-pretopological space,some important conclusions are obtained.This paper is consist of four chapter.Chapter one,the needed concepts in this paper,which are some basic concepts and some important conclusions on lattice thoery and L-pretopological space,are given,and the properties of the point of proximity in L-pretopological space are also studied.Chapter two,firstly,the concepts ofδ-open set,δ-closed set,δ-inner,δ-closure,δ-adherence point and so on are defined,its basic properties are disscussed, then given the relation between L-pretopological space andδ-pretopological space,and studied the problem of convergences in L-pretopological space;finally,δ-continuous order homorphism and its some basic properties are disscussed.Chapter three,the concepts of net and ideal ofδ-limit point andδ-cluster pointare defined in L-pretopological space,a few of its basic properties and equivalent characteraions are investigated,and gived the relation betweenδ-convergence fbr net and ideal.Chapter fbur,in L-pretopological space the concepts ofδ-separated set, δ-connected set andδ-connected space are introduced,and some characterizations of theδ-connectivity are given,then some of its important properties are investigated,it is proved that the connectedness is homemorphic and productive;thenδ- component is introduced in L-pretopological space and its properties are disscussed;lastly,the concept of localδ-connectedness is introduced in L-pretopological space and its properties are studied.