L-network Convergence And The G-zadeh Function

Nets, filters and Zadeh type functions are the most important tools in the L-Fuzzy topology, which are also widely investigated by many mathematicians. L-net and general Zadeh type functions can be regarded as the generalization of molecular nets and Zadeh type functions, respectively. They may employ much richer structure than that of the molecular nets and Zadeh type functions.In Chapter two, we discussed the convergence of L-net and its applications. First, the concepts of limit set, cluster set of L-net are introduced in the topo-logical molecular lattices, and many properties of molecular net are extended. Then, based upon L-net, T2 separation, compactness and subcompactness are characterrized in the topological molecular lattices.In Chapter three, we discussed G-Zadeh type functions. In section one, G-Zadeh type functions is introduced by means of generalized order-homomorphisms in complete lattice, it is also the generalization of Zadeh type functions, and G-Zadeh type functions is also a generalized order-homomorphisms. Many properties of G-Zadeh type functions are disscussed. In section two, based upon which, we obtained that many concepts, such as countablity, separation and compactness, are invariable characterization of G-homeomorphism in L-fuzzy topological spaces. In section three, given ft : X Xt (t T) is a projective mapping, gt : L - Lt is a monic and epi function. Based upon them, we get a new projective mapping, and it is also a G-Zadeh type function. Then we get G-Relative productive spaces, it is also the generalization of Relative productive spaces, and many properties of G-Relative productive spaces have been obtained. In the last section, we discussed topological properties of category G. First, .we introduced the concepts of category G. Then, in the fixed L = L1 (i = 1,2,...) and g = idL that of such category G, is investigated and many important results have been obtained, such as category G is a topological category over SET.