J-connectivity In L-topological Space And J-tight,

Connectedness and compactness are important notions in topology, in L-topology, owning to the complication of the gradation, the structure of connectedness and compactness are more complicated than general topology. In this thesis, first, we use the concept of J-closed set, J-closure which we introduced in L-topological spaces, and then we introduce the concept of J-connectedness, give some equivalent characterizations of J-connectedness and prove the K.Fan's theorem still hold for J-connectedness. Second, based on the concept of J-closed-remote neighborhood we introduce, we give the concept of J-compactness, study the characterization of J-compactness, and then discuss its property.