Topological Properties In Topological Rough Groups

A topological rough group G is a rough group G=(?)endowed with a topology,which is induced from the upper approximation space G,such that the product mapping f:G×G?(?)and the inverse mapping are continuous.By definition,topological rough gro up G is a topological group when its upper approximation is equal to itself.Topological grou ps have been studied extensively since last century,and many properties have been obtained However,for topological rough groups,there are many properties that are unknown until now As a generalization of topological rough groups,we naturally need to know whether some co nclusions in topological rough groups can be generalized to topological rough groups.This th esis mainly does the following workIn chapter 1,the background of topological rough groups and the research status at home and abroad are introduced,and some related definitions and theorems of topological rough gr oups are introducedIn chapter 2,the separation axioms of topological rough groups are explored,such as T0,T1,T2 etc.In addition,some basic properties of topological rough groups are studied,especiall y the neighborhood of the rough unit element of topological rough groupsIn chapter 3,some basic properties of topological rough subgroups are discussed.It is pro ved that the closure of topological rough subgroups of topological rough groups is topological rough subgroupsIn chapter 4,the concept of rough homomorphism is redefined and the open mapping the orem in topological rough groups is proved.