The Separation And Compactness Of Topological System

The topological sj'-stem is the most widely studied object in topology at present. Topological space ,spatialization of locale ,fuzzy topological space and topological molecular lattice are its special cases.One can also study Domain theory on denotational semantics of computer programming languages by using the topological system .In this paper , we have discussed some separations and compactness of Topological system from the view of general topology ,we have defined T0, T1, T2 , T3 , T4 in topological system .and discussed the equivalence relation of the sepatation between the topological system D and the topology space Spat(D) that induced by D .then taking LF-fuzzy topology space for example .we have also discussed the relation of the separation between (LX , ?) and (M*(LX) , ?, |=) that induced by (LX , ?) .At last .we got some result at the compactness of topological system .