Research On Compactness And Separations Of Generalized L-topological Spaces

Since the generalized L-topological spaces has been proposed,a series of meaningful research results has been made,and construct a theoretical framework of generalized L-topological spaces,but no one has studied the special compactness and weak separations of generalized L-topological spaces.Because the compactness and separations are important characteristics in topological spaces,therefore,based on the study of compactness and separations in L-topological spaces,this paper studied several kinds of compactness and separations in generalized L-topological spaces by literature analysis,analogy research and other reseach methods.The main contents of the full text are as follows:The first part discussed generalized almost N-compactness,generalized almost countable N-compactness and generalized countable paracompact in generalized L-topological spaces.Firstly,the definitions of generalized almost N-compact sets,generalized almost countable N-compact sets and generalized countable paracompact sets in generalized L-topological spaces are given by means of?-almost far domain family in generalized L-topological spaces.A series of properties of them are systematically discussed from the aspects of heritability,(weak)topological invariance and summability,and their relations with generalized countable compact sets and generalized Lindel(?)f sets are given.Secondly,a series of equivalent descriptions of them are given by using molecular network,almost r⁺-covering and almost r⁺-finite intersections.The second part discussed the generalized weak separation theorem of generalized L-topological spaces,the definition of generalized weak T₀ spaces,generarlized weak T₁ spaces,generalized weak T₂ spaces,genealized weak T₃ spaces and generalized weak T₄ spaces are presented in generalized L-topological spaces,proved the generalized weak T_i(i=0,1,2,3,4)spaces of generalized L-closed set and the generalized L-closed subspace hereditary,and they have the properties such as weak topological invariance;discussed the relationship between generalized weak separations and generalized separations.