| Fuzzy topological linear spaces as a new subject, constructed by Fuzzy topolotgy classical topological spaces, Lattice theory and Fuzzy mathematic. In contrast to classical topological linear spaces, Fuzzy topological endowed with richer content and entensive research prospect. At present, one of most studies is that extensive the theory of classical topological vector linear spaces to fuzzy topological linear spaces. Whereas the above extension is difficult. Since the characters of Fuzzy mathematics. How to overcome the difficulties as mentioned above? It is needed to set up the basic theory, which are match the development of Fuzzy mathematics, so that impel the Fuzzy topological vector linear spaces to achieve more development. But more and more types of problems and extension in Fuzzy topological vector linear spaces need our concern.More specially, the main results are as follow:1. Finite dimension of fuzzy normed linear spaces: First, the existing definitions of derivative for fuzzy norm are investigated, after that some characters about equivalent fuzzy norm are obtained. Secondly, some classical results about the normed linear spaces are generalized. Lastly, as the generalization of the finite dimension fuzzy normed linear spaces, fuzzy finite dimensional of fuzzy pre-normed linear spaces are definitioned and some properties about it are discussed.2. Fuzzy oparators: Firstly, some definitions of different types of fuzzy continuity of fuzzy operators are given. Relations between different fuzzy continuity are studied. Secondly, three types(weakly fuzzy bounded, strongly fuzzy bounded and uniformly fuzzy bounded) of fuzzy bounded operators are definded. Finally, Relations between different types of fuzzy continuity and different types fuzzy bounded are obtained.3. Fuzzy topological vector linear spaces: Firstly, we introduce the basic theory of fuzzy topological vector linear spaces. Secondly, the Hausdorff seperation property and equalivalence characterize about it in fuzzy topological vector spaces are discussed. Finally, we discuss the L-fuzzy topological vector spaces are completable and the completion theorem given.In this paper, by using fuzzy mathematic theory, some results of crisp topological vector linear spaces are generalized to fuzzy topological vector linear spaces. |
