In this paper it is proved that for all completely distributive lattices L. the category of L-fuzzifying topological spaces can be wmbedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a...In this paper it is proved that for all completely distributive lattices L. the category of L-fuzzifying topological spaces can be wmbedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a simultaneously bireflective and bicoreflective full subcategory.展开更多
The category of fuzzy pretopological spaces is introduced, and it is proved that this category is a well-fibred extensional topological construct, and it is a finally dense extension of the category of fuzzy topologic...The category of fuzzy pretopological spaces is introduced, and it is proved that this category is a well-fibred extensional topological construct, and it is a finally dense extension of the category of fuzzy topological spaces. Moreover this category contains both the category of pretopological spaces and the category of probabilistic neighbourhood spaces as simultaneously bireflective and bicoreflective full subcategories.展开更多
This paper presents a definition of L-fuzzifying nets and the related L-fuzzifying generalized convergence spaces. The Moore-Smith convergence is established in L-fuzzifying topology. It is shown that the category of ...This paper presents a definition of L-fuzzifying nets and the related L-fuzzifying generalized convergence spaces. The Moore-Smith convergence is established in L-fuzzifying topology. It is shown that the category of L-fuzzifying generalized convergence spaces is a cartesianclosed topological category which embeds the category of L-fuzzifying topological spaces as a reflective subcategory.展开更多
基金This work is supported by the Natural Science Foundation of Chinathe Foundation for Fellows Returned from Abroadthe Mathematical Center of the Education Ministry of China
文摘In this paper it is proved that for all completely distributive lattices L. the category of L-fuzzifying topological spaces can be wmbedded in the category of L-topological spaces (stratified Chang-Goguen spaces) as a simultaneously bireflective and bicoreflective full subcategory.
文摘The category of fuzzy pretopological spaces is introduced, and it is proved that this category is a well-fibred extensional topological construct, and it is a finally dense extension of the category of fuzzy topological spaces. Moreover this category contains both the category of pretopological spaces and the category of probabilistic neighbourhood spaces as simultaneously bireflective and bicoreflective full subcategories.
基金Supported by National Natural Science Foundation of China (Grant No.10926055)the Foundation of Hebei Province (Grant Nos. A2010000826+1 种基金 Z2010297)Foundation of Shijiazhuang University of Economics (GrantNo. XN201003)
文摘This paper presents a definition of L-fuzzifying nets and the related L-fuzzifying generalized convergence spaces. The Moore-Smith convergence is established in L-fuzzifying topology. It is shown that the category of L-fuzzifying generalized convergence spaces is a cartesianclosed topological category which embeds the category of L-fuzzifying topological spaces as a reflective subcategory.
