In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new...In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.展开更多
In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existe...In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.展开更多
In nonstandard enlargement, the separations are characterized by non- standard analysis methods in [0, 1J-topological spaces. Firstly, the monads of fuzzy point in [0, 1]-topological spaces are described with remote-n...In nonstandard enlargement, the separations are characterized by non- standard analysis methods in [0, 1J-topological spaces. Firstly, the monads of fuzzy point in [0, 1]-topological spaces are described with remote-neighborhoods in non- standard enlarged model. Then the nonstandard characterizations of separations in [0, 1]-topological space are given by the monads. At last, relations of these separations are investigated.展开更多
This paper formulates the category of L-fuzzy spaces and fuzzy functions.It shows that the category of topological spaces and continuous fuzzy functions is a direct generalization of TOP and LTOP Moreover,it defines t...This paper formulates the category of L-fuzzy spaces and fuzzy functions.It shows that the category of topological spaces and continuous fuzzy functions is a direct generalization of TOP and LTOP Moreover,it defines the concept of proximity space on L-fuzzy space and introduces its fundamental properties.A comparison between the classical case and the ordinary case has been outlined.展开更多
We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact,we define and study the notions of the L-double quotient spaces and the sum of L...We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact,we define and study the notions of the L-double quotient spaces and the sum of L-double fuzzy closure spaces. Finally,we study the additivity of two kinds of L-double fuzzy closure spaces.展开更多
In the present paper,sum operation on sum spaces of a family of L-topological spaces is defined. Fuzzy φψ-continuity from sum spaces of a family of L-topological spaces into L-product spaces and from sum spaces of a...In the present paper,sum operation on sum spaces of a family of L-topological spaces is defined. Fuzzy φψ-continuity from sum spaces of a family of L-topological spaces into L-product spaces and from sum spaces of a family of L-topological spaces into L-topological spaces are investigated.展开更多
In the present paper,φψ-continuous function on L-topological spaces and productive operation are defined.By means of this operation,we study fuzzy φψ-continuity from L-product spaces into L-product spaces and also...In the present paper,φψ-continuous function on L-topological spaces and productive operation are defined.By means of this operation,we study fuzzy φψ-continuity from L-product spaces into L-product spaces and also from L-topological spaces into L-product spaces.展开更多
In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characte...In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.展开更多
In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</...In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</sup></em> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of <em>L<sup>p</sup> p</em>-harmonic 1-forms on <em>M<sup>m</sup></em>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.展开更多
文摘In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.
基金Supported by the National Natural Science Foundation of China (10761007)
文摘In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.
基金The NSF (2007A12) of Shaanxi Provincethe Special Science Research Project (11JK0507) of Shaanxi Provincial Department of Edueation
文摘In nonstandard enlargement, the separations are characterized by non- standard analysis methods in [0, 1J-topological spaces. Firstly, the monads of fuzzy point in [0, 1]-topological spaces are described with remote-neighborhoods in non- standard enlarged model. Then the nonstandard characterizations of separations in [0, 1]-topological space are given by the monads. At last, relations of these separations are investigated.
文摘This paper formulates the category of L-fuzzy spaces and fuzzy functions.It shows that the category of topological spaces and continuous fuzzy functions is a direct generalization of TOP and LTOP Moreover,it defines the concept of proximity space on L-fuzzy space and introduces its fundamental properties.A comparison between the classical case and the ordinary case has been outlined.
文摘We prove the existence of both final L-double gradation fuzzy topological spaces and final L-double fuzzy closure spaces. From this fact,we define and study the notions of the L-double quotient spaces and the sum of L-double fuzzy closure spaces. Finally,we study the additivity of two kinds of L-double fuzzy closure spaces.
文摘In the present paper,sum operation on sum spaces of a family of L-topological spaces is defined. Fuzzy φψ-continuity from sum spaces of a family of L-topological spaces into L-product spaces and from sum spaces of a family of L-topological spaces into L-topological spaces are investigated.
文摘In the present paper,φψ-continuous function on L-topological spaces and productive operation are defined.By means of this operation,we study fuzzy φψ-continuity from L-product spaces into L-product spaces and also from L-topological spaces into L-product spaces.
文摘In this paper, the notion of almost fuzzy compactness is dened in L-fuzzy topological spaces by means of inequality, where L is a completely distributiveDeMorgan algebra. Its properties are discussed and many characterizations of it arepresented.
文摘In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.
文摘In this paper, we investigate the space of <em>L<sup>p</sup> p</em>-harmonic 1-forms on a complete noncompact orientable <em>δ</em>-stable hypersurface <em>M<sup>m</sup></em> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of <em>L<sup>p</sup> p</em>-harmonic 1-forms on <em>M<sup>m</sup></em>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.
