In this paper,it is discussed the induced extension of fuzzy topological spaces based on quasi-coincident structures of fuzzy points. Further,it is studied that the extensions of syntopogenous spaces. For a syntopogen...In this paper,it is discussed the induced extension of fuzzy topological spaces based on quasi-coincident structures of fuzzy points. Further,it is studied that the extensions of syntopogenous spaces. For a syntopogenous space (X,S) ,denote by T=((<<)~p}={<<_0}=S^(tp) and suppose fuzzy topological space (Y, T)is a weal insuced extension of fuzzy topological space (X, T). Does it exist a syntopogenous structure Son Y satisfyiny S|X～S and S^(tp)=T?. Importantly ,a general necessary condition is studied and two existence theorems are obtained. Moreover ,it is studied that the relationship between extensions and fuzzy refined syntopogenous structures.展开更多
文摘In this paper,it is discussed the induced extension of fuzzy topological spaces based on quasi-coincident structures of fuzzy points. Further,it is studied that the extensions of syntopogenous spaces. For a syntopogenous space (X,S) ,denote by T=((<<)~p}={<<_0}=S^(tp) and suppose fuzzy topological space (Y, T)is a weal insuced extension of fuzzy topological space (X, T). Does it exist a syntopogenous structure Son Y satisfyiny S|X～S and S^(tp)=T?. Importantly ,a general necessary condition is studied and two existence theorems are obtained. Moreover ,it is studied that the relationship between extensions and fuzzy refined syntopogenous structures.
