中文摘要：

通过研究Lukasiewicz模糊命题逻辑系统中极大相容理论的基本性质,证明了每个极大相容理论都是某赋值的核,反过来,每个赋值的核也都是一个极大相容理论.利用Lukasiewicz蕴涵算子的连续性在全体极大相容理论之集上引入了一种Fuzzy拓扑,证明了该Fuzzy拓扑空间是零维的、良紧的,但不是覆盖式紧的,其分明截拓扑空间是覆盖式紧的、可度量化的.

英文摘要：

By means of investigating basic properties of maximally consistent theories in Lukasiewicz fuzzy propositional logic,it is proved that each maximally consistent theory is the kernel of some valuation and vice versa,and consequently a structural characterization of maximally consistent theories in this logic is obtained.By virtue of the continuity of Lukasiewicz implication operator,a fuzzy topology as well as its cut topology on the set of all maximally consistent theories is introduced.It is proved that this fuzzy topological space is zero-dimensional and nice-compact,but not covering-compact,and its cut space is covering-compact and metrizable.