共查询到19条相似文献,搜索用时 46 毫秒
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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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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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给出L-幂集上LK-闭包系统的等价刻画。提出L-偏序集上闭包系统的概念并讨论其基本性质。最后,将经典偏序集和L-幂集上关于闭包算子和闭包系统的对应理论推广到L-偏序集上。 相似文献
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In this paper, as a generalization of uniform continuous posets, the concept of meet uniform continuous posets via uniform Scott sets is introduced. Properties and characterizations of meet uniform continuous posets are presented. The main results are:(1) A uniform complete poset L is meet uniform continuous iff ↑(U ∩↓ x) is a uniform Scott set for each x ∈ L and each uniform Scott set U;(2) A uniform complete poset L is meet uniform continuous iff for each∨∨x∈ L and each uniform subset S, one has x ∧S ={x ∧ s | s ∈ S}. In particular, a complete lattice L is meet uniform continuous iff L is a complete Heyting algebra;(3) A uniform complete poset is meet uniform continuous iff every principal ideal is meet uniform continuous iff all closed intervals are meet uniform continuous iff all principal filters are meet uniform continuous;(4) A uniform complete poset L is meet uniform continuous if L1 obtained by adjoining a top element1 to L is a complete Heyting algebra;(5) Finite products and images of uniform continuous projections of meet uniform continuous posets are still meet uniform continuous. 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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关于连续Domain权的进一步结果 总被引:8,自引:4,他引:4
在连续格理论的基础上探索连续Domain的权与相应Scott拓扑空间的权之间的关系,并进一步讨论其与相应的Lawson拓扑空间的权之间的关系,最后给出在连续Domain中W(P)=W(∑P)=W(AP)的结论。 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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连续Domain的遗传性及其不变性 总被引:1,自引:0,他引:1
引入Domain子空间的概念,得到Scott开集和闭集都是Domain的子空间。证明连续Domain或代数Domain对开子空间和闭子空间都是可遗传的。证明连续Domain或代数Domain在保Waybelow序的Scott连续映射下保持不变。 相似文献
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讨论了交连续dcpo的遗传性和不变性,证明了如下结论:(1)交连续dcpo对于开子空间和闭子空间都是可遗传的;(2)交连续dcpo在加最大元和去最小元运算下保持交连续性;(3)交连续dcpo的收缩核为交连续dcpo.另外,给出了交连续的主理想刻画的一个直接证明;构造了反例说明交连续dcpo对于主滤子是不可遗传的;也构造了反例说明所有主滤子都交连续的一个dcpo,自身不必是交连续的. 相似文献
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定义相容Domain的子Domain与子空间等概念,得到Scott开集和Scott闭集都是相容Domain的子Domain与子空间的结论,证明了相容连续Domain或相容代数Domain对开子空间和闭子空间都是可遗传的。 相似文献
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给出代数L-domain和强core紧空间以及连续L-domain和core紧空间的刻画。 相似文献
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In this paper the new concept of B-posets is introduced. Some properties
of B-posets and FS-posets are examined. Main results are: (1) Posets obtained
from B-posets (FS-posets) by eliminating a proper upper subset, adding two or
more finitely many incomparable maximal elements, taking vertical sums w.r.t.
a maximal element are also B-posets (FS-posets); (2) A poset is a(n) B-domain
(FS-domain) iff it is a Lawson compact B-poset (FS-poset); (3) The directed
completions of B-posets (FS-posets) are B-domains (FS-domains); (4) The category
B-POS (FS-POS) of B-posets (FS-posets) and Scott continuous maps
is cartesian closed and has the category B-DOM (FS-DOM) of B-domains
(FS-domains) and Scott continuous maps as a full reflective subcategory. 相似文献
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Hanfeng Li 《Journal of Functional Analysis》2009,256(10):3368-2350
We show that for any co-amenable compact quantum group A=C(G) there exists a unique compact Hausdorff topology on the set EA(G) of isomorphism classes of ergodic actions of G such that the following holds: for any continuous field of ergodic actions of G over a locally compact Hausdorff space T the map T→EA(G) sending each t in T to the isomorphism class of the fibre at t is continuous if and only if the function counting the multiplicity of γ in each fibre is continuous over T for every equivalence class γ of irreducible unitary representations of G. Generalizations for arbitrary compact quantum groups are also obtained. In the case G is a compact group, the restriction of this topology on the subset of isomorphism classes of ergodic actions of full multiplicity coincides with the topology coming from the work of Landstad and Wassermann. Podle? spheres are shown to be continuous in the natural parameter as ergodic actions of the quantum SU(2) group. We also introduce a notion of regularity for quantum metrics on G, and show how to construct a quantum metric from any ergodic action of G, starting from a regular quantum metric on G. Furthermore, we introduce a quantum Gromov-Hausdorff distance between ergodic actions of G when G is separable and show that it induces the above topology. 相似文献