共查询到18条相似文献,搜索用时 46 毫秒
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将一致小于关系移植到一般偏序集上,同时引入了上界小于关系,定义了偏序集的一致连续性和上界连续性.给出了一致连续偏序集的等价刻画,探讨了一致连续偏序集所具有的性质.主要结果有:(1)证明了偏序集上的一致连续性,上界连续性与s-超连续性均等价;(2)在交半格条件下,偏序集的一致连续性等价于它的每一主理想一致连续;(3)在并半格条件下,偏序集的一致连续性蕴含连续性,反之不成立;(4)一致完备的一致连续偏序集均是连续bc-dcpo,且每个主理想均为完全分配格;(5)在一致完备的条件下,一致连续性对主滤子,对闭区间,对Scott S-集以及对一致连续投射像均是可遗传的.文中也构造了若干实用的反例. 相似文献
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利用偏序集上的半拓扑结构,引入了交C-连续偏序集概念,探讨了交C-连续偏序集的性质、刻画及与C-连续偏序集、拟C-连续偏序集等之间的关系.主要结果有:(1)交C-连续的格一定是分配格;(2)有界完备偏序集(简记为bc-poset)L是交C-连续的当且仅当对任意x∈L及非空Scott闭集S,当∨S存在时有x∧∨S=∨{x∧s:s∈S};(3)完备格是完备Heyting代数当且仅当它是交连续且交C-连续的;(4)有界完备偏序集是C-连续的当且仅当它是交C-连续且拟C-连续的;(5)获得了反例说明分配的完备格可以不是交C-连续格,交C-连续格也可以不是交连续格. 相似文献
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研究偏序集上的测度拓扑以及与其它内蕴拓扑间的关系,利用测度拓扑刻画了偏序集的连续性.构造了反例说明存在完全分配格,其上的测度拓扑不是连续格从而不是局部紧拓扑. 相似文献
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证明φ-完备偏序集是(强)P连续的当且仅当该偏序集的任一主理想是(强)φ-连续的。在φ-完备偏序集中利用φ-S集族生成f-Scott拓扑,并由此引入φ-交连续偏序集概念。证明φ-完备偏序集是P交连续的当且仅当该偏序集的任一主理想是φ-交连续的。 相似文献
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引入了Zs-相客集系统的概念,讨论了Zs-相客连续偏序集的一系列性质.证明了Zs-相容连续偏序集范畴对偶等价于完全分配格范畴的一个满子范畴. 相似文献
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引入了FS-偏序集和连续L-偏序集概念,探讨了FS-偏序集和连续L-偏序集的性质.主要结果有(1)每一FS-偏序集都是有限上集生成的,因而是Scott紧的;(2)证明了FS-偏序集(连续L-偏序集)的定向完备化是FS-偏序集(连续L-偏序集);(3)一个偏序集是一个FS-Domain当且仅当它为Lawson紧的FS-偏序集;(4)FS-偏序集(连续L-偏序集)去掉部分极大元后还是FS-偏序集(连续L-偏序集). 相似文献
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In this paper, posets which may not be dcpos are considered. In terms of the Scott topology on posets, the new concept of
quasicontinuous posets is introduced. Some properties and characterizations of quasicontinuous posets are examined. The main
results are: (1) a poset is quasicontinuous iff the lattice of all Scott open sets is a hypercontinuous lattice; (2) the directed
completions of quasicontinuous posets are quasicontinuous domains; (3) A poset is continuous iff it is quasicontinuous and
meet continuous, generalizing the relevant result for dcpos.
Supported by the NSF of China (10371106, 10410638) and by the Fund (S0667-082) from Nanjing University of Aeronautics and
Astronautics. 相似文献
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We endow orthocomplemented posets with a binary operation–an abstract symmetric difference of sets–and we study algebraic
properties of this class, . Denoting its elements by ODP, we first investigate on the features related to compatibility in ODPs. We find, among others,
that any ODP is orthomodular. This explicitly links with the theory of quantum logics. By analogy with Boolean algebras, we then ask if (when) an ODP is set representable. Though
we find that general ODPs do not have to be set representable, many natural ODPs are shown to be. We characterize the set-representable
ODPs in terms of two valued morphisms and prove that they form a quasivariety. This quasivariety contains the class of pseudocomplemented
ODPs as we show afterwards. At the end we ask whether any orthomodular poset can be converted or, more generally, enlarged
to an ODP. By countre-examples we answer these questions to the negative.
The authors acknowledge the support of the research plan MSM 0021620839 that is financed by the Ministry of Education of the
Czech Republic and the grant GAČR 201/07/1051 of the Czech Grant Agency. 相似文献
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In This paper, we prove that the uniform space (X, ψ) is complete if and only if for every remote point p in *X, there exists a pseudo-metric d in the lattice set of ψ and a positive number r such that d(p, q) ≥ r for each q ∈ X. 相似文献
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本文证明了格的极小生成元集一定是最小生成元集且只能是非零完全并既约元全体,证明了分配格具有最小生成元集的必要条件是它满足并无限分配律.本文还证明了完全Heyting代数具有最小生成元集当且仅当它是强代数格,证明了完备格是强代数格当且仅当它和它的对偶格均是具有最小生成元集的分配格. 相似文献
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Let X be a Banach space, S be a compact Hausdorff space and Y be a U-proximinal subspace of X. We prove that C(S,Y) is locally uniformly strongly proximinal in C(S,X) and the corresponding metric projection map is Hausdorff metric continuous. 相似文献
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Large Sets of Wrapped K–K Hamilton Cycle Decompositions of Complete Bipartite 3‐Uniform Hypergraphs 下载免费PDF全文
Using the Katona–Kierstead (K–K) definition of a Hamilton cycle in a uniform hypergraph, we investigate the existence of wrapped K–K Hamilton cycle decompositions of the complete bipartite 3‐uniform hypergraph and their large sets, settling their existence whenever n is prime. 相似文献
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With every subset selection for posets, there is associated a certain ideal completion . As shown by Erné, such completions help to extend classical results on domains and similar structures in the absence of
the required joins. Some results about –predistributive or –precontinuous posets and –continuous functions are summarized and supplemented. In particular, several central results on function spaces in domain
theory are extended to the setting of productive closed subset selections. The category FSBP, in which objects are finitely separated and upper bounded posets and arrows are continuous functions between them, is shown to be cartesian closed.
This research is supported by the National Natural Science Foundation of China, 10471035. 相似文献