The concept of relative N-compactness is defined and characterized in terms ofnets. It is shown that the relative N-compactness is hereditary with respect to L-fuzzy setsand the relative N-compactness is L-good extens...The concept of relative N-compactness is defined and characterized in terms ofnets. It is shown that the relative N-compactness is hereditary with respect to L-fuzzy setsand the relative N-compactness is L-good extension. Some connections between the N-compactness and the relative N-compactness are investigated. It is also proved that inducedrelative N-compact spaces are productive, and the product of finite relative compact sets isrelative compact.展开更多
In this paper, we prove that （L^X,5） is T0,T1, T2, regular （T3）, normal （T4） and completely regular spaces if and only if （R（L）^X, ω（δ）） is T0, T1, T2, regular （T3）, normal （T4） and completely regula...In this paper, we prove that （L^X,5） is T0,T1, T2, regular （T3）, normal （T4） and completely regular spaces if and only if （R（L）^X, ω（δ）） is T0, T1, T2, regular （T3）, normal （T4） and completely regular spaces, respectively, and （L^X,δ） is N-compact if and only if （R（L）^X, ω（δ）） is N-compact.展开更多
It is no doubt that the researches on the N-compactness in[1] and [2] are a nice and important achievement in L-fuzzy topology. There is a natural and interesting question about the N-compactness——the sheaf structur...It is no doubt that the researches on the N-compactness in[1] and [2] are a nice and important achievement in L-fuzzy topology. There is a natural and interesting question about the N-compactness——the sheaf structures of N-compact sets. It is proved that, for weakly induced Hausdorff space, the N-compactness of L-fuzzy set A in the upper展开更多
In this paper we give a characteristic property of convergence of nets in induced I(L)-topological spaces and a simplified proof for the N-compactness being an I(L)-'good extension'.
基金Supported by the National Natural Science Foundation of China(10271069)Supported by the Science Foundation of Weinan Teacher's College(03YKS002)
文摘The concept of relative N-compactness is defined and characterized in terms ofnets. It is shown that the relative N-compactness is hereditary with respect to L-fuzzy setsand the relative N-compactness is L-good extension. Some connections between the N-compactness and the relative N-compactness are investigated. It is also proved that inducedrelative N-compact spaces are productive, and the product of finite relative compact sets isrelative compact.
基金Foundation item： the National Natural Science Foundation of China （No. 10471083） the Natural Science Foundation of Zhejiang Education Committee （No. 20060500）.
文摘In this paper, we prove that （L^X,5） is T0,T1, T2, regular （T3）, normal （T4） and completely regular spaces if and only if （R（L）^X, ω（δ）） is T0, T1, T2, regular （T3）, normal （T4） and completely regular spaces, respectively, and （L^X,δ） is N-compact if and only if （R（L）^X, ω（δ）） is N-compact.
基金Project supported partly by the National Natural Science Foundation of China
文摘It is no doubt that the researches on the N-compactness in[1] and [2] are a nice and important achievement in L-fuzzy topology. There is a natural and interesting question about the N-compactness——the sheaf structures of N-compact sets. It is proved that, for weakly induced Hausdorff space, the N-compactness of L-fuzzy set A in the upper
基金National Natural Science Foundation of China (10371079)
文摘In this paper we give a characteristic property of convergence of nets in induced I(L)-topological spaces and a simplified proof for the N-compactness being an I(L)-'good extension'.
