Some Properties Of Generalized L - Topological Spaces

Generalized L-topological spaces which was introduced by Bai(S.Z.Bai. Generalized L-topological space[J]. Journal of Intelligent and Fuzzy Systems, 2015, 28: 301-309.) was a kind of weak L-topological spaces in 2015. And some basic concepts and basic properties were researched in generalized L-topological spaces. Then Bai introduced generalized L-separations and generalized L-Urysohn spaces and generalized compact axioms defined by remote neighborhood family in generalized L-topological spaces.Thus, the basic framework of generalized L-topological spaces had been preliminary established. In this thesis, on the basis of these results, we will mainly discuss on the basic concepts and basic properties of quasi open sets, quasi closed sets, quasi interior and closure operators, quasi continuous mappings, quasi compactness and countable L-compactness in generalized L-topological spaces.The key contents of the thesis comprise three parts.In first part, this paper firstly introduces the concepts of quasi open sets, quasi closed sets, quasi interior and closure operators in generalized L-topological spaces. Next, our aim is to continue the research for quasi continuous mappings by basic definitions in generalized L-topological spaces and give to some characterizations and relationships among them.In second part, the basic concepts of ?-quasi-net, ?-quasi-filter, quasi cover form,finite intersection property and quasi compactness introduce in generalized L-topological spaces. Then, quasi compactness is described by ?- quasi-net, ?- quasi-filter, quasi cover form and finite intersection property. In addition, we discuss other properties of quasi-compact..In third part, the generalized countable L-compact sets and generalized Lindelof sets are introduced in generalized L-topological spaces. They are described by cover form and finite intersection property. They are preserved under generalized L-continuous mapping,inherited for L-closed subsets, and finitely additive.