Fell-拓扑的伪紧性（英文）

设X是拓扑空间，CL（X）表示X的所有非空闭子集的族，本文得到了下述结果：在CL（X）上的Fell-拓扑是伪肾的当且仅当X是feebly-紧或者非局部紧或者非σ－紧，由此得到了对于伪紧性不是闭遗传的两类新的拓扑空间。     

MV-代数的素滤子MV-拓扑空间

在MV-方体[0,1]X的子集Ω上引进MV-拓扑结构,并套论MV-拓扑空间的紧性、Hausdorff分离性等拓扑性质.细致地讨论MV-代数的素滤子集上的MV-拓扑空间(M,ΩM),证明素滤子MV-拓扑空间是紧Hausdorff MV-空间,并且它还是良紧空间.作为应用,证明一个σ-完备格M是MV-代数当且仅当M同构于某个Stone MV-空间的MV-开闭集格.     

L-拓扑空间的单点超F紧化

给出L-拓扑空间的单点超F紧化的一种具体作法,以及局部超F紧性的定义,并证明了:(1)局部超F紧性是L-好推广;(2)一个L-拓扑空间是局部超F紧T2空间当且仅当其单点超F紧化空间是超F紧T2空间;(3)单点超F紧化在同胚意义下是唯一的。     

凸幂Domain的极大点的注记

本文讨论了连续Domain D的极大点Max(D)的紧子集Com(Max(D))与凸幂Domain CD的极大点Max(CD)一一对应的条件以及Max(CD)上拓扑的性质, 证明了当X为局部紧Hausdorff空间时,X的上空间UX的凸幂Domain C(UX)的极大点Max(C(UX))与Com(Max(UX))(即X的紧子集)一一对应.X的上空间UX上的Lawson拓扑与X紧子集上的Vietoris拓扑相同,并且与Max(C(UX))带有C(UX)上的相对Scott拓扑同胚.     

超空间与原空间动力系统之间的关系

设(X,d,f)为拓扑动力系统,其中X为局部紧可分的可度量化空间,d为紧型度量,f为完备映射,用2X表示由X的所有非空闭子集构成的集族,(2X,ρ,2f)为由(X,d,f)所诱导的赋予hit-or-miss拓扑的超空间动力系统.本文引入了余紧点传递和弱拓扑传递的定义.特别的,在X满足一定的条件时,给出了点传递,弱拓扑传递和余紧点传递之间的关系,并研究了(X,d,f)的余紧传递点,回复点和几乎周期点分别与(2X,ρ,2f)的传递点,回复点和几乎周期点之间的蕴含关系.这些结论丰富了赋予hit-or-miss拓扑的超空间的研究内容.     

分形空间的局部紧性及网极限

对于完备度量空间 (X ,d) ,研究了X的局部紧性与相应分形空间 (H(X) ,h)的局部紧性之间的关系 ,得到结论 :(H(X) ,h)是局部紧的当且仅当X是局部紧的 .另一方面 ,给出了 (H(X) ,h)中收敛网的极限通过并、交及闭包运算的表示 .     

L-预拓扑空间的强连通集和局部强连通L-预拓扑空间

定义L-预拓扑空间中的强连通L-子集以及L-预拓扑空间的局部强连通性,证明了它们和拓扑空间中的连通子集以及局部连通性拓扑空间有类似的性质,证明了局部强连通L-预拓扑空间和连续映射构成的范畴L-LSCPS是topological construct.     

L-拓扑空间的弱局部强F紧性及单点强F紧化

以R.Lowen的强F紧性为基础,定义了L-拓扑空间的弱局部强F紧性及单点强F紧化,推广了有关弱局部紧拓扑空间和拓扑空间的单点紧化的若干结果,证明了L-拓扑空间的弱局部强F紧性是拓扑空间的弱局部紧性的L-推广。     

局部Z-空间和Z-连续空间

对于一般广义子集系统Z,引入了局部Z-空间和Z-连续空间的概念,讨论了局部Z-空间的基本性质;基于收敛网,给出了局部Z-空间的等价刻画,证明了X为Z-连续空间当且仅当X为局部Z-空间。     

hit-or-miss拓扑上的度量:直接扩充

设E是Hausdorff局部紧第二可数拓扑空间.用F表示由E的所有闭子集构成的超空间,其上赋予hit-or-miss拓扑.本文引入了E上的紧型度量和F上保距扩张的概念,建立了E上度量是紧型的充分必要条件,并且证明了E上任何一个紧型度量度可以直接扩充为F上的保距度量.     

On Uniformly Locally Compact Quasi-Uniform Hyperspaces

We characterize those Tychonoff quasi-uniform spaces for which the Hausdorff-Bourbaki quasi-uniformity is uniformly locally compact on the family of nonempty compact subsets of X. We deduce, among other results, that the Hausdorff-Bourbaki quasi-uniformity of the locally finite quasi-uniformity of a Tychonoff space Xis uniformly locally compact on if and only if Xis paracompact and locally compact. We also introduce the notion of a co-uniformly locally compact quasi-uniform space and show that a Hausdorff topological space is -compact if and only if its (lower) semi-continuous quasi-uniformity is co-uniformly locally compact. A characterization of those Hausdorff quasi-uniform spaces for which the Hausdorff-Bourbaki quasi-uniformity is co-uniformly locally compact on is obtained.     

Topological Representations of Distributive Hypercontinuous Lattices

The concept of locally strong compactness on domains is generalized to general topological spaces. It is proved that for each distributive hypercontinuous lattice L, the space SpecL of nonunit prime elements endowed with the hull-kernel topology is locally strongly compact, and for each locally strongly compact space X, the complete lattice of all open sets O（X） is distributive hypercontinuous. For the case of distributive hyperalgebraic lattices, the similar result is given. For a sober space X, it is shown that there is an order reversing isomorphism between the set of upper-open filters of the lattice O（X） of open subsets of X and the set of strongly compact saturated subsets of X, which is analogous to the well-known Hofmann-Mislove Theorem.     

Normal Vietoris Implies Compactness: A Short Proof

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.     

On Weak Well-posedness of the Nearest Point and Mutually Nearest Point Problems in Banach Spaces

Let G be a nonempty closed subset of a Banach space X. Let B(X) be the family of nonempty bounded closed subsets of X endowed with the Hausdorff distance and ■, where the closure is taken in the metric space(B(X), H). For x ∈ X and F ∈ BG(X), we denote the nearest point problem inf ■ by min(x, G) and the mutually nearest point problem inf■ by min(F, G). In this paper, parallel to well-posedness of the problems min(x, G) and min(F, G) which are defined by De Blasi et al., we further introduce the weak well-posedness of the problems min(x, G) and min(F, G). Under the assumption that the Banach space X has some geometric properties, we prove a series of results on weak well-posedness of min(x, G) and min(F, G). We also give two sufficient conditions such that two classes of subsets of X are almost Chebyshev sets.     

Fell—拓扑的某些性质

刻画了Fell-拓扑的某些性质以及Fell-拓扑和拓扑收敛的关系。     

ON THE THEOREM OF ARROW-BARANKIN-BLACKWELL FOR WEAKLY COMPACT CONVEX SET

This papeer studies the known density theorem of Arrow-Barankin-Blackwell. The following main result is obtained: If X is a Hausdorff locally convex Topological space and C belong to X is a closed convex cone with bounded base, then for every nonempty weakly compact convex subset A, the set of positive proper efficient points of A is dense in the set of efficient points of A.     

ON THE THEOREM OF ARROW-BARANKIN-BLACKWELL FOR WEAKIY COMPACT CONVEX SET

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集值动力系统中的混合性和混沌

设(X,d)是紧致度量空间.设(K,H)是X中所有非空紧子集所组成的空间,并赋予由d导出的Hausdorff度量H.主要探讨了拓扑动力系统(X,G)的混合性、混沌和集值动力系统(K,G)的混合性、混沌之间的关系,其中G是拓扑群.     

Embedding theorems for classes of convex sets

Rådström's embedding theorem states that the nonempty compact convex subsets of a normed vector space can be identified with points of another normed vector space such that the embedding map is additive, positively homogeneous, and isometric. In the present paper, extensions of Rådström's embedding theorem are proven which provide additional information on the embedding space. These results include those of Hörmander who proved a similar embedding theorem for the nonempty closed bounded convex subsets of a Hausdorff locally convex vector space. In contrast to Hörmander's approach via support functionals, all embedding theorems of the present paper are proven by a refinement of Rådström's original method which is constructive and does not rely on Zorn's lemma. This paper also includes a brief discussion of some actual or potential applications of embedding theorems for classes of convex sets in probability theory, mathematical economics, interval mathematics, and related areas.