Some Topological Properties Of Fuzzy Topological Spaces

From the date C.L.Chang published his first paper which introduced the concept of fuzzy topological spaces, the study of fuzzy topology walks gradually from the mimicry of the inception up creative road. The characteristics of the hierarchial structure makes it have differ from to general topology. Furthermore, the affiliation to the complete lattice algebra gave it the vitality. It became from naive to maturity, superficial to deep. Being an independent subject, we can say that it is already a deep leaf luxuriant.In this paper, we introduce foundamental knowledge of fuzzy topological spaces.For one thing, in this paper, based on the concepts of the σ— fuzzy discrete base, the necessity conditions for metrization of the fuzzy topological spaces is obtained. Moreover, one sufficency conditions for metrization of the fuzzy topological space is also proved by the Embedding Lemma. Finally, some properties of the fuzzy unit interval FI are investigated.For another thing, we define a new kind of paracompactness which is called m—para-compactness. The relationship between this para-compactness and the others were discussed, some of its properties such as good extension, hereditary with respect to closed subsets and weakly topological property were obtained.Still another, the m—Lindelo|¨f property is proved.At last, after the introduction of the concept of fuzzy sets by Zadeh, several reserches were conducted on the generalization of the notion of fuzzy sets. The idea of L-fuzzy sets was published by Goguen takes fuzzy sets as a special case when L=[0,l]. On the other hand, Atanassov introduced the idea of intuition-istic fuzzy sets, many works by the same author and his colleagues appeared in the literature. Coker introduced the idea of the topology of intuitionistic fuzzy sets. Wang Guojun proved that the concepts of intuitionistic fuzzy sets and intuitionistic L-fuzzy sets, the concepts of L-fuzzy sets are equivalent, we study the category of fuzzy topological spaces and the category of intuitionistic fuzzy topological spaces, furthermore, we prove the equivalence of these two categories.