Research Of Compactness And Separations In L-bi-pretopological Spaces

L-bi-pretopological spaces is generalization of L-pretopological spaces.It is more general than L-bitological spaces and has some good properties.Compactness and separations are important concepts in topological spaces,therefore,based on the study of compactness and separations in L-pretopological spaces and L-bitopological spaces,the compactness and separations in L-bi-pretopological spaces are discussed using literature analysis,analogical research and other method,The main contents of the full text are as follows:The first part pairwise N-compactness,coparacompactness,and sheaf coparacompactness are discussed in L-bi-pretopological spaces.Firstly,the concept of L-bi-pretopological spaces is given,in which the spaces of "-pre-romote neighborhood family,locally finite,and strongly locally finite are used to define(countably)pairwise N-compact sets,(countably)coparacompact sets,and(countably)sheaf coparacompact sets;Secondly,their basic properties and equivalent characterizations are discussed;Finally,a series of topological properties of them closed hereditary,integrability,weak topological invariance,and "L-good generalization" are systematically discussed.The second part separations is discussed in L-bi-pretopological spaces.Firstly,the definitions of weak matching Ti spaces and matching Ti spaces are given in L-bi-pretopological spaces(i=0,1,2,3,4);The relationship between the various separations was discussed,it is proved that(weak)matching Ti(i=0,1,2,3,4)spaces are hereditary with respect to their closed subspaces,and has weak topological invariance and other properties;Secondly,we discuss the separations of L-bi-pretopological space product spaces;Finally,the relationship between the separations in weakly induced L-bi-pretopological spaces and the separations in their base spaces is discussed.