Relative Separation And Relative Compactness In L-Fuzzy Topological Spaces

Properties of the relative topology have always played essential roles in topological spaces. Until now, some important results have been obtained in general topological spaces, especially on the relative separation axioms and relative compactness. In this paper, we discuss properties of relative topology in L-fuzzy topological spaces. Because separation properties and compactness are very important in topological spaces, we mainly study relative separation axioms and relative compactness in L-fuzzy topological spaces. As the layer structure of lattice, relative separation properties and relative compactness in L-fuzzy topological spaces are more complex than that in general topological spaces. A series of results of relative separation properties and relative compactness are obtained in L-fuzzy topological spaces.Chapter one defines some notions and gives some theorems about general topology and L-fuzzy topology we will use in this paper.In chapter two, the notions of relative separation axioms T-1, sub-T0, T0, T1,T2 regular(T3), normal(T4) are introduced firstly, and then we study their propertiesrespectively. Some equivalent characterizations of these relative separation axioms are given. In the and, the relationship between separation and relative separation is discussed.In chapter three, firstly, the concept of relative strong separation ST1,S-Hausdorff (ST2), S-regular (ST3), S-normal (ST4) is introduced, and then some equivalentcharacterizations of relative strong separation properties are given respectively. Secondly, we investigate relative strong separation properties and discuss the relationship between strong separation and relative strong separation.In chapter four, we introduce several kinds of relative compactness in L-fuzzy topological spaces firstly. The relationship between these kinds of relative compactness is dicciiscod. By using net and cover we study various properties of these kinds of relative compactness. In the end, we prove that these kinds of compactness are equivalent when the L-fuzzy topological space is induced.