区间映射与其诱导函数包络序列熵关系

研究了区间映射的拓扑序列熵与其诱导的函数包络上的拓扑序列熵之间的关系.证明了区间映射诱导的函数包络的拓扑序列熵只能为0或+∞,并且当区间映射的拓扑序列熵大于0时,其诱导的函数包络上的拓扑序列熵为+∞.     

新型拓扑KKM定理与等价形式及其应用

在不具线性结构拓扑空间—广义区间空间—中得到了新型拓扑KKM定理及其几个等价形式.作为应用,本文研究了广义区间空间中一类抽象形式变分不等式解的存在性问题.     

区间映射的链回归点的可链点集

主要讨论区间映射的链回归点的可链点集与链等价集的关系,证明了:若区间映射的拓扑熵是零,则它的链回归点的可链点集与链等价集相等.此外还得到了区间映射有正拓扑熵的几个等价条件.     

内蕴拓扑与Hutton单位区间的细致化

本文把连续格理论引入对Hutton单位区间I(L)的研究,简捷地证明了I(L)的若干性质.在此基础上,利用I(L)的承集上的内蕴拓扑对I(L)的拓扑进行了细致化,定义了一个具有诸多良好性质的新不分明单位区间I(L),称为H(λ)单位区间.我们定义了相应的H(λ)完全正则性并建立了H(λ)式 Stone-Cech紧化理论.     

基于自反关系的区间值模糊近似空间诱导的拓扑结构

给出了论域U上自反的区间值模糊关系R诱导拓扑的一种新方法,并与胡凯的关于模糊紧性与粗集拓扑的研究中R诱导拓扑的方式进行了比较。结果表明:(1)后者需要R具有传递性才能生成拓扑,而前者则不需要此条件;(2)当R满足传递性时,两种方式生成的拓扑是相同的。     

树映射有异状点的一个充要条件

讨论了树上连续自映射的拓扑熵与非稳定流形之间的关系． 证明了：树上连续自映射有异状点的充要条件是其拓扑熵大于零． 因而推广了区间上连续自映射的一个结果．     

关于连续区间映射的敏感依赖性

首先证明:若区间映射f是敏感依赖的,则f的拓扑熵ent(f)>0.然后通过引入一种扩张映射进一步证明了敏感依赖的区间映射的拓扑熵的下确界为0,即,上式中拓扑熵的下界0是最优的.最后通过实例展示稠混沌、Spatio-temporal混沌、Li-Yorke敏感及敏感性之间是几乎互不蕴含的.     

广义区间空间中参数型非紧KKM定理及其在经济平衡问题上的应用

在不具线性结构的拓扑空间———广义区间空间———中证明了集值映像参数型非紧的 KKM定理,用本文结果研究了极大极小问题和拓扑型广义经济Shafer Sonneischein平衡存在问题.     

超实数域^＊R的拓扑结构

研究了超实数域上两种有用的拓扑－Ｑ－拓扑和Ｓ－拓扑。证明了以下结果：空间（＊Ｒ，Ｑ）是完全不连通的；＾＊Ｒ的Ｑ－紧子集只有有限集；＾＊Ｒ中的每一个银河是（＊Ｒ，Ｓ）的一个连通分支；＾＊Ｒ中的每一个具有有限长度的区间（不必是闭的）都是Ｓ－紧的，同时也纠正了《Ｍａｔｈ．Ｊａｐｏｎｉｃａ》上一篇论文中关于＾＊Ｒ上的Ｑ－拓扑的性质的一些错误。     

区间值模糊滤子范畴

讨论区间值模糊滤子范畴IVF和Hausdorff区间值模糊滤子范畴IVFHau中乘积、余积、等子、余等子存在性及构造。证明IVF和IVFHau都不是完备范畴而IVF是余完备范畴。也证明IVF不仅有许多弱拓扑满子范畴,也有许多非弱拓扑满子范畴。     

On continuous noncomplete lattices

We consider noncomplete continuous and algebraic lattices and prove that finitely generated free lattices are algebraic. We also study the Lawson topology, the second most important topology in the theory of continuous domains, on finitely presented lattices. In particular, we prove that algebraic finitely presented lattices are linked bicontinuous and the Lawson topology on these lattices coincides with the interval topology. Several examples of non-distributive and noncomplete algebraic and continuous lattices are given in the paper. Received April 5, 2000; accepted in final form December 12, 2000.     

Ricci curvature in the neighborhood of rank-one symmetric spaces

We study the Ricci curvature of a Riemannian metric as a differential operator acting on the space of metrics close (in a weighted functional spaces topology) to the standard metric of a rank-one noncompact symmetric space. We prove that any symmetric bilinear field close enough to the standard may be realized as the Ricci curvature of a unique close metric if its decay rate at infinity (its weight) belongs to some precisely known interval. We also study what happens if the decay rate is too small or too large.     

Upper semifinite hyperspaces as unifying tools in normal Hausdorff topology

In this paper we use the upper semifinite topology in hyperspaces to get results in normal Hausdorff topology. The advantage of this point of view is that the upper semifinite topology, although highly non-Hausdorff, is very easy to handle. By this way we treat different topics and relate topological properties on spaces with some topological properties in hyperspaces. This hyperspace is, of course, determined by the base space. We prove here some reciprocals which are not true for the usual Vietoris topology. We also point out that this framework is a very adequate one to construct the ?ech-Stone compactification of a normal space. We also describe compactness in terms of the second countability axiom and of the fixed point property. As a summary we relate non-Hausdorff topology with some facts in the core of normal Hausdorff topology. In some sense, we reinforce the unity of the subject.     

Priestley Spaces, Quasi-hyperalgebraic Lattices and Smyth Powerdomains

We introduce the concept of quasi-hyperalgebraic lattice and prove that a complete lattice is a Priestley space with respect to the interval topology if and only if it is quasi-hyperalgebraic. Some characterizations of quasi-hyperalgebraic lattices are presented. We also prove that the Smyth powerdomain of a quasi-hyperalgebraic lattice is hyperalgebraic.     

Interval topology on effect algebras

In this paper, we study the interval topology on effect algebras, and prove that effect algebra operation on Hilbert space effect algebra E(H) is not jointly continuous under the interval topology.     

On products with the unit interval

We investigate the question which compact convex sets are homeomorphic to their product with the unit interval. We prove it in particular for the space of probability measures on any infinite scattered compact space and for the half-ball of a non-separable Hilbert space equipped with the weak topology. We also show examples of compact spaces for which it is not the case.     

Lattice Im plication Homom orphism inIm plication Filter Spaces

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偏序集上的测度拓扑与稠拓扑

In this paper,the concepts of the essential topology and the density topology of dcpos are generalized to the setting of general posets.Basic properties of the essential topology and relations with other intrinsic topologies are explored.Comparisons between the density topology and the measurement topology are made.Via the essential topology,the density topology and the measurement topology,we obtain properties and characterizations of bases of continuous posets.We also provide some new conditions for a continuous poset to be an algebraic poset.     

Preorderable topologies and order-representability of topological spaces

We furnish characterizations of topologies that coincide with the lower topology or with the order topology of some total preorder defined on a set. Leaning on these characterizations we introduce some applications to the study of continuous and semicontinuous order-representability properties of topological spaces.