共查询到17条相似文献,搜索用时 93 毫秒
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对完备格引入半素极小集的概念,证明完备格L为半连续格当且仅当L中的每个元在L中存在半素极小集,给出半连续格的两个序同态扩张定理. 相似文献
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给出广义λ超连续格的几个刻画。特别地,我们证明了完备格L上的λ-区间拓扑θλ(L)是严格T2的L是广义λ超连续格L上的关系是广义λ正则的。 相似文献
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Yang Zhongqiang 《东北数学》1994,(3)
TheCartesianClosednessoftheCategoryCDLandFunctionSpacesonTopologicalCDL'sYangZhongqiang(杨忠强)(DepartmentofMathematics,ShaanxiN... 相似文献
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定义了广义完全极小集,并证明了L为广义完全分配格与它的每个元都有广义完全极小集等价。在广义完全分配格中,给出了保广义完全极小集映射的几个等价刻画,并且在此基础上得到了广义完全分配格上的两个相应扩张定理。 相似文献
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Strongly Pseudoalgebraic Lattices 总被引:3,自引:0,他引:3
In the recent twenty years,the generalizations of continuous lattices have attracted aconsiderable deal of attention (see [1 -6] ) .The so-called generalized continuous lat-tices(GCL) (see[2 ] ) is one of the most successful generalizations of continuous lat-tices.In 1 990 ,Venugopalan gave the definition of pseudoalgebraic lattice and provedthat a complete lattice is a compact totally order-disconnected(Preistley) space with re-spect to the Lawson topology if and only if it is a pseadoalgeb… 相似文献
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Hongjun Zhou Bin Zhao 《Fuzzy Sets and Systems》2012,187(1):33-57
Bosbach and Rie?an states on residuated lattices both are generalizations of probability measures on Boolean algebras. Recently, two types of generalized Bosbach states on residuated lattices were introduced by Georgescu and Mure?an through replacing the standard MV-algebra in the original definition with arbitrary residuated lattices as codomains. However, several interesting problems there remain still open. The first part of the present paper gives positive answers to these open problems. It is proved that every generalized Bosbach state of type II is of type I and the similarity Cauchy completion of a residuated lattice endowed with an order-preserving generalized Bosbach state of type I is unique up to homomorphisms preserving similarities, where the codomain of the type I state is assumed to be Cauchy-complete. Consequently, many existing results about generalized Bosbach states can be further strengthened. The second part of the paper introduces the notion of relative negation (with respect to a given element, called relative element) in residuated lattices, and then many issues with the canonical negation such as Glivenko property, semi-divisibility, generalized Rie?an state of residuated lattices can be extended to the context of such relative negations. In particular, several necessary and sufficient conditions for the set of all relatively regular elements of a residuated lattice to be special residuated lattices are given, of which one extends the well-known Glivenko theorem, and it is also proved that relatively generalized Rie?an states vanishing at the relative element are uniquely determined by their restrictions on the MV-algebra consisting of all relatively regular elements when the domain of the states is relatively semi-divisible and the codomain is involutive. 相似文献
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研究了一般剩余格(未必可换)与布尔代数的关系,给出剩余格成为布尔代数的一系列充要条件.同时,进一步将这些结果推广到只含有蕴涵运算的有界psBCK-代数中,证明了在一定条件下由psBCK-代数可诱导出有界格且构成布尔代数. 相似文献
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进一步研究了余剩余格的一些性质,在此基础上证明了正则余剩余格与对合BCK-格是两个等价的代数系统。所得结果将有助于深入了解正则余剩余格的代数结构,也为相关多值逻辑系统的研究提供又一途径。 相似文献