共查询到20条相似文献,搜索用时 296 毫秒
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定义了拟Z-极小集,并证明了拟Z-连续Domain的每个元都有拟Z-极小集,在拟Z-连续Domain中,给出了保拟Z-极小集映射的几个等价刻画,并且在此基础上,运用Rudin性质,得到了拟Z-连续Domain上的两个相应扩张定理. 相似文献
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引入WZ-双小于关系, 以此为基础给出WZ-Domain的概念, 讨论它的基本性质, 证明当子集系统Z满足一定条件时, WZ-Domain上的WZ-双小于关系具有插入性.其次, 在Z-完备偏序集上定义WZ-Scott拓扑, 证明在一定条件下一个映射关于该拓扑是连续映射当且仅当该映射保定向的Z集之并. 最后对WZ-Domain上的WZ-Scott拓扑的性质进行研究, 证明对一类子集系统,WZ-Scott拓扑空间是Sober空间当且仅当该拓扑空间具有Rudin性质. 相似文献
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Z-拟连续domain上的Scott拓扑和Lawson拓扑 总被引:16,自引:0,他引:16
对一般子集系统Z,引入了Z-拟连续domain的概念,证明了Z-完备偏序集P是Z-拟连续的当且仅当P上的Z-Scott拓扑σZ(P)在集包含序下是超连续格;Z-拟连续domain P上的Z-Scott拓扑σZ(P)是Sober的当且仅当σZ(P)具有Rudin性质,P贼予Z-Lawson拓扑λZ(P)是pospace,且若P上的Z-Lawson开上集是Z-Scott开的,Z-Lawson开下集是下拓扑开的,则(P,λZ(P))为严格完全正则序空间. 相似文献
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对一般子集系统Z,引入了Z-拟连续domain的概念,证明了Z-完备偏序集P是Z-拟连续的当且仅当P上的Z-Scott拓扑σ_z(P)在集包含序下是超连续格;Z-拟连续domain P上的Z-Scott拓扑σ_z(P)是Sober的当且仅当σ_z(P)具有Rudin性质,P赋予Z-Lawson拓扑λ_z(P)是pospace;且若P上的Z-Lawson开上集是Z-Scott开的,Z-Lawson开下集是下拓扑开的,则(P,λ_z(P))为严格完全正则序空间。 相似文献
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在定向完备偏序集(即dcpo)上引入了拟基的概念,给出了拟基的若干刻画并在此基础上定义了拟连续Domain的权。探讨了拟连续Domain的权与该拟连续Domain上赋予内蕴拓扑时的拓扑空间的权之间的关系。 相似文献
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拟Z-连续domain和Z-交连续domain 总被引:11,自引:0,他引:11
对一般子集系统Z,引入了Rudin性质、拟Z-连续domain及Z-交连续 domain的概念,讨论了它们的基本性质.特别是Z-连续性、拟Z-连续性、 Z-交连 续性和Z-Lawson拓扑之T2性之间的相互关系. 证明了当子集系统Z满足一定条件 时,拟Z-连续domain P上的Z-way below关系Z具有插入性质, P上的Z-Lawson 拓扑λZ(P)是T2的,且P可用Z-Lawson同态嵌入到某方体之中.文中给出了一个 domain P,其上的Lawson拓扑λ(P)是T2的,但P不是拟连续性domain. 相似文献
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基于一般子集系统Z,引入拟Z-代数domain的概念,研究了拟Z-代数domain的一些映射性质,并讨论了拟Z-代数domain与拟Z-连续domain之间的关系及拟Z-代数domain的乘积。 相似文献
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Z-Continuous Posets and Their Topological Manifestation 总被引:3,自引:0,他引:3
Marcel Erné 《Applied Categorical Structures》1999,7(1-2):31-70
A subset selection Z assigns to each partially ordered set P a certain collection Z P of subsets. The theory of topological and of algebraic (i.e. finitary) closure spaces extends to the general Z-level, by replacing finite or directed sets, respectively, with arbitrary Z-sets. This leads to a theory of Z-union completeness, Z-arity, Z-soberness etc. Order-theoretical notions such as complete distributivity and continuity of lattices or posets extend to the general Z-setting as well. For example, we characterize Z-distributive posets and Z-continuous posets by certain homomorphism properties and adjunctions. It turns out that for arbitrary subset selections Z, a poset P is strongly Z-continuous iff its Z-join ideal completion Z P is Z-ary and completely distributive. Using that characterization, we show that the category of strongly Z-continuous posets (with interpolation) is concretely isomorphic to the category of Z-ary Z-complete core spaces. For suitable subset selections Y and Z, these are precisely the Y-sober core spaces. 相似文献
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给出强Z-连续domain和Z-代数domain的一个刻画及一个范畴性质--余反射性质. 相似文献
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We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property. 相似文献
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Tamás Erdélyi 《Constructive Approximation》2016,43(3):357-369
Littlewood polynomials are polynomials with each of their coefficients in \(\{-1,1\}\). A sequence of Littlewood polynomials that satisfies a remarkable flatness property on the unit circle of the complex plane is given by the Rudin–Shapiro polynomials. It is shown in this paper that the Mahler measure and the maximum modulus of the Rudin–Shapiro polynomials on the unit circle of the complex plane have the same size. It is also shown that the Mahler measure and the maximum norm of the Rudin–Shapiro polynomials have the same size even on not too small subarcs of the unit circle of the complex plane. Not even nontrivial lower bounds for the Mahler measure of the Rudin–Shapiro polynomials have been known before. 相似文献
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Richard P. Stanley 《Order》1984,1(1):29-34
An elementary, self-contained proof of a result of Pouzet and Rosenberg and of Harper is given. This result states that the quotient of certain posets (called unitary Peck) by a finite group of automorphisms retains some nice properties, including the Sperner property. Examples of unitary Peck posets are given, and the techniques developed here are used to prove a result of Lovász on the edge-reconstruction conjecture.Supported in part by a National Science Foundation research grant. 相似文献
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Anders Björner 《Journal of Combinatorial Theory, Series A》1981,30(1):90-100
This paper is concerned with homotopy properties of partially ordered sets, in particular contractibility. The main result is that a noncomplemented lattice with deleted bounds is contractible. The paper also presents (i) the homology of final sets and cutsets, (ii) a generalization to posets of Rota's crosscut theorem, (iii) contractibility proofs for some classes of posets of interest in fixed point theory, and (iv) a simple characterization of the Cohen-Macaulay property for dismantlable lattices. 相似文献