Cong-hua Yan

Generalization of Kolmogoroff' s theorem to L-topological vector spaces

In this paper, the concept of L-fuzzy normed linear spaces is introduced and some of its properties are studied. Then we give a necessary and sufficient condition for L-topological vector spaces to be L-fuzzy normable. This is a generalization of Kolmogoroffs theorem in the classical topological vector spaces to L-topological vector spaces.

Locally bounded L -topological vector spaces

The purpose of this paper is to introduce the concept of locally bounded L-topological vector spaces and prove that each locally bounded L-vector topology on X can be determined by an L-fuzzy quasi-norm.

Induced I ( L )-fuzzy topological vector spaces

Abstract In this paper we introduce and study the induced I ( L )-fuzzy topological vector spaces. The following main result is proved: If ( L X , δ ) is an L -fuzzy topological vector space, then ( I ( L ) X , ω I ( L ) ( δ )) is an I ( L )-fuzzy topological vector space, where I ( L ) is the fuzzy unit interval and ω I ( L ) ( δ ) is the induced I ( L )-fuzzy topology of the L -fuzzy topology δ . Furthermore, we also prove that the induced I ( L )-fuzzy topological vector spaces ( I ( L ) X , ω I ( L ) ( δ )) preserve the product and quotient space as well.

I-fuzzy topological groups

In this paper, the concept of I-fuzzy topological groups is introduced and some of its properties are discussed. Considering Jin-ming Fangs notion of I-fuzzy quasi-coincident neighborhood system [Fuzzy Sets and Systems 147 (2004) 317-325], we obtained a characterization of I-fuzzy topological groups in terms of the corresponding I-fuzzy quasi-coincident neighborhood system at identity element. Finally, we showed that the category of I-fuzzy topological groups and fuzzy continuous homomorphisms is isomorphic to the category of antichain I-topological groups and I-continuous homomorphisms; and the category I-fuzzy topological groups is topological over the category of groups with respect to the forgetful functor.

Generalization of inductive topologies to L -topological vector spaces

In this paper, using the theory of L-topological vector spaces, we study some properties of inductive topologies determined by the family of L-fuzzy linear order-homomorphisms defined by Fang Jin-xuan (J. Fuzzy Math. 4(1) (1996) 93), and give a characterization of inductive topologies determined by a single L-fuzzy linear order-homomorphism. As an example, we point out the quotient L-topology of L-tvs is an inductive topology.

Level topologies of fuzzifying topological linear spaces and their applications

In this paper, some properties of level topologies of fuzzifying topological linear spaces are discussed. Then the characterizations of fuzzy boundedness and fuzzy precompactness are obtained. They may be considered as reply to the problem suggested by Qiu [Fuzzifying topological linear spaces, Fuzzy Sets and Systems 147 (2004) 249-272]. As applications, in Menger probabilistic normed spaces with respect to t-norm minimum, unified fuzzifying topological characterizations of probabilistic bounded, probabilistic semi-bounded, probabilistic unbounded sets, and probabilistic precompact, probabilistic semi-precompact, probabilistic unprecompact sets are proved, respectively.

Fuzzy L-bornological spaces

The main purpose of this paper is to introduce a concept of fuzzy L-bornological spaces, and an equivalent characterization theorem of these spaces is obtained. Finally we prove that inductive topology of fuzzy L-bornological spaces is fuzzy L-bornological.

I(L)-topological vector spaces and its level topological spaces☆

In this paper the relationship between I(L)-topological vector spaces and its level topological spaces is discussed, the main result of this paper is to give a method which generates an I(L)-topological vector space by a co-tower of vector L-topologies. This result is a generalization of previous results published in this journal by the same authors.

The uniform boundedness principle in L -topological vector spaces

In this paper, we introduce and study the equicontinuity of a family of L -fuzzy linear order-homomorphisms. we prove a generalization of the uniform boundedness principle in the classical topological vector spaces to L -topological vector spaces.

Linear operators in fuzzifying topological linear spaces

In this paper, some of the properties of continuous linear operators between fuzzifying topological linear spaces are studied. Particularly, the equivalence between continuity and boundedness is investigated and the closed graph theorem is generalized to the fuzzifying setting. Finally some properties of the initial fuzzifying topologies determined by a family of linear operators are investigated.