The Research On Several Problems Of Generalized Topology

A i deal topological space is a new topological space, which is the general topological space deduced from ideal. it have similar properties with general topological space and have its special characters.The reseach of covering property is an important issue for the general topology, the research method of replacing open sets with generalized open sets is employed to introduce the new covering characteristics.we thecan study the feature characteristics and the relationship with the generalized separation axioms.In the paper ,we introduce new open sets :weekly-β-Iopen sets.we obtain its properties and discuss weekly-β-I continuity mappings. moreover,we introduce *-connected spaces in ideal topological spaces,and study its characteristics, obtain some properties. in addition, the research method of replacing open sets with generalized open sets is employed to introduce the concept of Seq ? lindel ?f spaces, and give some characterizations.as well as the relationship between the property of Seq-lindelof spaces and generalized separation axioms.This paper is parted into four chapters.In the first chapter, we introduce the background knowledge of related.In the second chapter, we introduce the concept of weekly-β-I open sets and weekly-β-I continuous mappings, give some characterizations .the main results obtain in the third chapter as follows, theorem2.3.6, theorem 2.4.4, theorem 2.4.9.In the third chapter, we introduce the concept of *-connected spaces and study its nature and feature .the main results obtain in the third chapter as follows, theorem 3.3.5, theorem3.3.15, theorem3.5.4.In the four chapter,we introduce the concept of Seq-lindelof spaces, and give some characterizations, the main result obtain in the four chapter as follows: theorem 4.3.4; theorem 4.3.8; theorem4.4.10; theorem 4.4.12.