共查询到19条相似文献,搜索用时 93 毫秒
1.
2.
3.
4.
5.
本文利用引入的KS性质,刻划了那些其Scott拓扑可由开滤子生成的分配备格,该结果也是对[1]中一公开问题的一种解答.本文的刻划定理对于判定分配备格的Scott拓扑是否与Scott开滤子拓扑一致具有较强的可操作性,应用该刻划定理给出大量非连续格,其Scott拓扑具有开滤子基. 相似文献
6.
R_0代数的滤子理论 总被引:1,自引:0,他引:1
在R0代数中引入了正蕴涵滤子、奇异滤子、MV滤子的概念,讨论了这些滤子的性质及关系.得到了:在R0代数上,蕴涵滤子、正蕴涵滤子、布尔滤子是等价的;奇异滤子与MV滤子是等价的;正蕴涵滤子是奇异滤子,但反之不真. 相似文献
7.
讨论了当格蕴函代数L是完全分配格时蕴涵运算的一些性质,在格蕴函代数L上引入了集合的蕴函传递性概念,证明了格蕴涵代数的滤子满足蕴涵传递性和替换定理,即格蕴涵代数的滤子满足命题逻辑的三段论推理规则的替换定理。 相似文献
8.
9.
10.
在Girard Quantale中引入了模糊滤子和模糊关联滤子的概念,研究了Girard Quantale中模糊滤子和模糊关联滤子的一些性质,给出了Girard Quantale中模糊关联滤子的若干等价刻画,探讨了模糊关联滤子与模糊布尔滤子之间的关系. 相似文献
11.
John L. Bell 《Mathematical Logic Quarterly》1999,45(1):135-143
Some aspects of the theory of Boolean algebras and distributive lattices–in particular, the Stone Representation Theorems and the properties of filters and ideals–are analyzed in a constructive setting. 相似文献
12.
引入偏序集的相对极大滤子的概念,证明在任意条件交半格中一个滤子是相对极大滤子当且仅当它是滤子格的完全交不可约元.一个格是分配的当且仅当每一个相对极大滤子都是素滤子.随后研究了Heyting代数中相对极大滤子的刻画,最后定义和研究了完全并既约生成格. 相似文献
13.
This paper is devoted to the discussion of filters in residuated lattices. The lattice structure of filters in residuated lattice was established. It is proved that the set of all filters forms a distributive lattice. Also, the concept of prime filter in residuated lattice was proposed and some equivalent conditions about prime filter were given. 相似文献
14.
Fuzzy蕴涵代数的MP滤子 总被引:9,自引:3,他引:6
给出了Fuzzy蕴涵代数(简称FI代数)上的MP滤子的等价刻画和由非空子集生成的MP滤子的表示定理; 探讨了FI代数的MP滤子与偏序滤子之间的关系; 证明了一个FI代数上全体MP滤子之集在集合包含序下构成一个分配连续(代数)格,从而构成一个Frame. 相似文献
15.
A near-Heyting algebra is a join-semilattice with a top element such that every principal upset is a Heyting algebra. We establish a one-to-one correspondence between the lattices of filters and congruences of a near-Heyting algebra. To attain this aim, we first show an embedding from the lattice of filters to the lattice of congruences of a distributive nearlattice. Then, we describe the subdirectly irreducible and simple near-Heyting algebras. Finally, we fully characterize the principal congruences of distributive nearlattices and near-Heyting algebras. We conclude that the varieties of distributive nearlattices and near-Heyting algebras have equationally definable principal congruences. 相似文献
16.
Lawrence W. Baggett Jennifer E. Courter Kathy D. Merrill 《Applied and Computational Harmonic Analysis》2002,13(3):201
The classical constructions of wavelets and scaling functions from conjugate mirror filters are extended to settings that lack multiresolution analyses. Using analogues of the classical filter conditions, generalized mirror filters are defined in the context of a generalized notion of multiresolution analysis. Scaling functions are constructed from these filters using an infinite matrix product. From these scaling functions, non-MRA wavelets are built, including one whose Fourier transform is infinitely differentiable on an arbitrarily large interval. 相似文献
17.
针对分配格与模格的格等式定义问题,得知了二条件是定义分配格与模格的最少条件,并进一步证明了Sholander's basis是定义分配格的最短最少变量格等式,最后又从分配格和模格的基本定义出发给出了新的分配格的二条件和三条件等价定义等式及模格的二条件与三条件等价定义等式. 相似文献
18.
We extend a constructive proof of the Eisenbud–Evans–Storch theorem, developed in a previous work by Coquand, Schuster, and Lombardi, from the affine to the projective case. The main tool is that of distributive lattices, which allows us to replace the classical topological arguments by more algebraic and constructive ones. Given a suitable graded ring, we work in the distributive lattice in which the prime filters correspond to the homogeneous prime ideals. The proof presented here is one of the first examples of concrete results obtained using this tool. 相似文献
19.
We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators. 相似文献