L-topological Space Completely Normal Separation And L-fuzzy Algebra Structure

In this paper, the main purpose is to study (strong) completely normal separation axiom in L-topological spaces and several algebra structures on L-Fuzzy algebra. This paper is made up of two parts. In the first part, several kinds of completely normal separation axioms in L-topological spaces are researched. In the second part, we study up on several algebra structures on L-Fuzzy algebra.In the first part, the concepts of the completely normal spaces and strong completely normal spaces in L-topological spaces are defined, which are the generalization of the completely normal spaces in general topological spaces. They are some good properties such as hereditary, weakly homeomorphism invariant properties, good L-extension, but they aren't producible in general. Moreover, their several sufficient and necessary conditions in induced spaces are presented.In the second part, several fuzzy algebra structures, such as L- Fuzzy subfield, L-Fuzzy linear spaces over L- Fuzzy subfields, L- Fuzzy algebra over L- Fuzzy subfields, L- Fuzzy sublattice group etc, are defined. Subsequently, based on several kinds of level cut sets in [8], their some nature properties are discussed. Finally, application of these equivalent characterizations by means of Zadeh function is presented.