Basic homogeneity in the class of zero-dimensional compact spaces

We show that under the continuum hypothesis there is a compact zero-dimensional space which admits a base of pairwise homeomorphic clopen subsets but it is not an h-homogeneous space (i.e. not all of its nonempty clopen subsets are homeomorphic), partially answering a question of M.V. Matveev. Under Jensen's ? principle, we can even make the space hereditarily separable and hence, by a result of Matveev, an S-space.     

Frolík decompositions for lattice-ordered groups

Frolík’s theorem says that a homeomorphism from a certain kind of topological space to itself decomposes the space into the clopen set of fixed points together with three clopen sets, each of whose images is disjoint from the original set. Stone’s theorem translates this result to a corresponding theorem about the Riesz space of continuous functions on the topological space. We prove a theorem analogous to that for Riesz spaces in the much more general setting of (possibly noncommutative) lattice-ordered groups and group-endomorphisms. The groups to which our result applies satisfy a weak condition, introduced by Abramovich and Kitover, on the polars; the images of our endomorphisms have a kind of order-density on their polars; the double polars of the images are cardinal summands; and the endomorphisms themselves are disjointness-preserving in both directions. We explain how to extend our result to larger groups to which it does not apply, and, to give additional insight, we provide many examples.     

Almost locatedness in uniform spaces

A weak form of the constructively important notion of locatedness is lifted from the context of a metric space to that of a uniform space. Certain fundamental results about almost located and totally bounded sets are then proved.     

Regular Ordering and Existence of Minimum Points in Uniform Spaces and Topological Groups

It is defined the locally order convexity of an ordered uniform space and an ordered topological group and is investigated its relation to the existence of minimum points of denumerable, complete lower bounded sets.     

一致结构的单子及其应用

讨论了乘积一致结构的单子的刻画 .利用一致结构的单子给出了 Cauchy网及含小集集族的非标准特征 .作为应用给出一致空间几个重要定理的离散化证明 .     

Van Douwen's problem on 0-dimensional images of ordered compacta

A compact 0-dimensional space has a -separating rank 1 family of clopen sets iff it is the continuous image of a compact 0-dimensional linearly ordered space.

     

Topological representation of posets

There is a canonical imbedding of a poset into a complete Boolean lattice and hence into a Boolean lattice. This gives it a representation as a collection of clopen sets of a Boolean space. There are reflective functions from a category of distributive posets to the subcategories of distributive and Boolean lattices and consequently a topological dual equivalence that extends the Stone duality of Boolean lattices.Presented by B. Jonsson.     

Epigraphical and Uniform Convergence of Convex Functions

We examine when a sequence of lsc convex functions on a Banach space converges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlevé-Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear functionals are shown to also hold for lsc convex functions. For example, a sequence of lsc convex functions converges uniformly on bounded sets to a continuous affine function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of .

     

Preservation of completeness by some continuous maps

We show that a metrizable space Y is completely metrizable if there is a continuous surjection f:X→Y such that the images of open (clopen) subsets of the (0-dimensional paracompact) ?ech-complete space X are resolvable subsets of Y (in particular, e.g., the elements of the smallest algebra generated by open sets in Y).     

Arzelà's Theorem and strong uniform convergence on bornologies

In 1883 Arzelà (1983/1984) [2] gave a necessary and sufficient condition via quasi-uniform convergence for the pointwise limit of a sequence of real-valued continuous functions on a compact interval to be continuous. Arzelà's work paved the way for several outstanding papers. A milestone was the P.S. Alexandroff convergence introduced in 1948 to tackle the question for a sequence of continuous functions from a topological space (not necessarily compact) to a metric space. In 2009, in the realm of metric spaces, Beer and Levi (2009) [10] found another necessary and sufficient condition through the novel notion of strong uniform convergence on finite sets. We offer a direct proof of the equivalence of Arzelà, Alexandroff and Beer-Levi conditions. The proof reveals the internal gear of these important convergences and sheds more light on the problem. We also study the main properties of the topology of strong uniform convergence of functions on bornologies, initiated in Beer and Levi (2009) [10].     

模糊一致体

定义了模糊一致体概念,研究了它与模糊拓扑体的关系及它与模糊一致空间的关系;给出了借助于体的模糊子集族对模糊一致体的刻画,还引入了模糊一致子体,模糊一致商体与模糊一致体的直积;并讨论了它们的分离性.     

交一致连续偏序集

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.     

广义α-Stable过程的像集和图集的一致维数

研究了未必具有随机一致Holder条件的N指标d维广义α-stable过程的像集和图集的一致维数问题,并在一定条件下得到了N指标d维广义α-stable过程像集约一致Hausdorff维数和一致Packing维数的上、下界,图集的一致Hausdorff维数和一致Packing维数的上界,包含了多指标α-stable过程和广义布朗单相应的结果．     

模糊一致环

本文定义了模糊一致环概念,研究了它与模糊拓扑环的关系及它与模糊一致空间的关系;给出了借助于环的模糊子集族对模糊一致环的刻画,还引入了模糊一致子环,模糊一致剩余类环与模糊一致环的直积;并讨论了它们的分离性.     

二维序贯均匀设计方法的拓展研究

将二维序贯均匀设计方法拓展到三维空间,扩展到三维的序贯均匀设计可用于优化的三因子试验设计问题,从而达到既减少试验次数,又提高试验精度的目的.     

Musielak-Orlicz序列空间的一致Gateaux可微性

利用Musielak-Orlicz函数列的某些性质,给出了赋Luxemburg范数的Musielak-Orlicz序列空间是有一致Gateaux可微性的充要条件及赋Orlicz范数的Musielak-Orlicz序列空间是弱一致凸的判别准则.     

基于正交表的均匀Latin Hypercube设计及其构造

Orthogonal array-based uniform Latin hypercube design(uniform OALHD) is a class of orthogonal array-based Latin hypercube designs to have the best uniformity. In this paper, we provide a less computational algorithm to construct uniform OALHD in 2-dimensional space from Bundschuh and Zhu(1993). And some uniform OALHDs are con- structed by using our method.     

���ڸ��ʿռ�������������ռ��е��������һ�¿ɻ��Ե�һ��ע��

In this note we discuss uniform integrability of random variables. In a probability space, we introduce two new notions on uniform integrability of random variables, and prove that they are equivalent to the classic one. In a sublinear expectation space, we give de La Vall\'{e}e Poussin criterion for the uniform integrability of random variables and do some other discussions.     

Strong Nearness Frames Having Enough Cauchy Filters

We prove results establishing sufficient conditions for the sum of two nearness frames to have enough Cauchy filters. From these results and the fact that, in the category of strong nearness frames having enough Cauchy filters and uniform frame maps, complete spatial frames form a coreflective subcategory, follow a variety of results where the open-sets contravariant functor from topological spaces to frames transforms products into sums and inverse limits into direct limits.