The Study On Some Topological Properties In Fuzzifying Topology

The thesis mainly discusses the topological properties of delta openset in fuzzifying topological spaces and the continuity&product spacesof the L-fuzzifying topological spaces. The brief introduction of theessay is as follows.(1) In1991, scholar of Ying Mingsheng put forward the fuzzifyingtopological spaces from a various logic angle. Afterwards, lots of scholarsresearched on the fuzzifying topological widely and deeply. For example,they extended the open set in classical to fuzzifying topological spaces.With the method of using continuous valued semantics of logic, the thesisis in the framework of the fuzzifying topological spaces, which leads tothe concepts of delta closure, delta open set, etc. The essay researcheson some topological properties for further study, and delta-convergence,delta-compactness as well.(2) In1980, U.H hle put forward (M, L)-fuzzy topology. Afterwards,plenty of scholars did some meaningful researches on (2, L)-fuzzytopology (L-fuzzifying topology). When L=[0,1],(2, L)-fuzzy topologyis a fuzzifying topology which is what Ying put forward in1991.In2010,Fathei M. Zeyada and A.M.Zahran extended some results of fuzzifyingtopological spaces to the L-fuzzifying topological spaces of L which iscomplete residuated lattice-valued logic.Based on the conceptsabove,The essay will keep on studying the continuity and product spacesof the L-fuzzifying topology.