共查询到20条相似文献,搜索用时 62 毫秒
1.
2.
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
3.
本文证明了:对corecompact空间X和具有最小元的有界完备连续DCPOL,[X→L]上的Isbell拓扑与Scott拓扑重合.并且构造两个反例说明:若L不具有最小元,或L具有最小元但不满足有界完备性,则[X→L]上的Isbell拓扑与Scott拓扑不必重合. 相似文献
4.
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
5.
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
6.
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
7.
连续偏序集及其Smyth幂的几个等权定理 总被引:2,自引:1,他引:1
推广连续D om a in的权的概念到连续偏序集上,探讨连续偏序集的权、相应内蕴拓扑的权、定向完备化的权以及Sm yth幂D om a in的权间的关系。得到了几个等权定理:(1)连续偏序集的权与其上Scott拓扑、L aw son拓扑的权相等;(2)连续偏序集的权与其定向完备化的权相等;(3)无穷连续D om a in的权与其Sm yth幂D om a in的权相等;(4)有限D om a in的权小于或等于它的Sm yth幂D om a in的权。 相似文献
8.
9.
群的一个Domain结构 总被引:1,自引:1,他引:0
群可以通过在其上赋予循环群拓扑构造群的Domain模型,从而实现群的可计算性。群上的循环群偏序集及其对偶都是连续的偏序集,这个连续偏序集是代数Domain的充分必要条件是群的单位元是代数元。如果在pseudo-有限的群G及其循环群偏序集的对偶£^op[G]上分别赋予循环群拓扑和Scott拓扑,那么恒同函数是连续的。 相似文献
10.
借助α-ω聚点与α-聚点概念给出可数强F紧集的两个刻画定理,进而讨论可数强F紧集在L值Zadeh型函数下的逆不变性,证明了可数强F紧集与强F紧集的乘积是可数强F紧的。 相似文献
11.
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
12.
We introduce a framework of approximable disjunctive propositional logic, which is the logic that results from a disjunctive propositional logic by adding an additional connective. The Lindenbaum algebra of this logic is an approximable dD-algebra. We show that for any approximable dD-algebra, its approximable filters ordered by set inclusion form a continuous L-domain. Conversely, every continuous L-domain can be represented as an approximable dD-algebra. Moreover, we establish a categorical equivalence between the category of approximable dD-algebras with approximable dD-algebra morphisms and that of continuous L-domains with Scott-continuous functions. This extends Abramsky's Domain Theory in Logical Form to the world of continuous L-domains. As an application, we give an affirmative answer to an open problem of Chen and Jung. 相似文献
13.
Mathematical Notes - In the paper, we consider the problem of uniform approximation of a continuous function defined on a compact metric space $$X$$ by elements of the sum of two algebras in the... 相似文献
14.
For an absolutely continuous probability measure μ on R d and a nonnegative integer k , let tilde s k (μ ,origin ) denote the probability that the convex hull of k+d+1 random points which are i.i.d. according to μ contains the origin bf 0 . For d and k given, we determine a tight upper bound on tilde s k (μ ,origin ) , and we characterize the measures in R d which attain this bound. As we will see, this result can be considered a continuous analogue of the Upper Bound Theorem for the maximal number of faces of convex polytopes with a given number of vertices. For our proof we introduce so-called h -functions, continuous counterparts of h -vectors of simplicial convex polytopes. Received April 14, 2000, and in revised form October 6, 2000. Online publication June 20, 2001. 相似文献
15.
Yuguang Xu 《Journal of Approximation Theory》2001,113(2):324
The purpose of this note is to show a new generalization of the continuous approximate selection theorem of F. Deutsch and P. Kenderov (1983, SIAM J. Math. Anal.14, 185–194). 相似文献
16.
In this paper, by applying a vector-valued inequality we obtained a decomposition theorem on Herz spaces over locally compact Vilenkin groups with new range 0 < q≤1. 相似文献
17.
Martin Man-chun Li 《Journal of Geometric Analysis》2014,24(3):1490-1496
Let M be a compact n-dimensional Riemannian manifold with nonnegative Ricci curvature and mean convex boundary ?M. Assume that the mean curvature H of the boundary ?M satisfies H≥(n?1)k>0 for some positive constant k. In this paper, we prove that the distance function d to the boundary ?M is bounded from above by \(\frac{1}{k}\) and the upper bound is achieved if and only if M is isometric to an n-dimensional Euclidean ball of radius \(\frac{1}{k}\) . 相似文献
18.
本文刻画了紧邻域扩充性质的等价条件,由此条件得到如果X是具有紧邻域扩充性质的可度量化的拓扑空间,则Fk(X)={A?X:|A|≤k}也具有紧邻域扩充性质,此处Fk(X)上的拓扑是由Hausdorf度量所诱导出的拓扑 相似文献
19.
Marilyn Breen 《Geometriae Dedicata》1998,71(2):111-117
For a family C of nonempty compact sets in the plane, the following conditions are equivalent:(1) Every two (not necessarily distinct) members of C have a connected union and every three (not necessarily distinct) members of C have a simply connected union.(2) C is a family of simply connected sets such that every two (not necessarily distinct) members of C have a connected intersection and every three (not necessarily distinct) members of C have a nonempty intersection.If either set of conditions is satisfied, then { C : C in C } is nonempty, simply connected, and connected. Furthermore, if the collection C is finite, then it is also true that { C : C in C } is simply connected. 相似文献