诱导极限中的弱紧集

本文研究了诱导极限中的弱集与紧集，我们给出了诱导极限ｉｎｄｉｍ Ｅｎ中每个弱紧集含于且弱紧于某Ｅｎ的一些条件。     

Eberlein mulian定理在局部凸空间中的推广

设（Ｅ，Ｔ）是一个分离的局部凸空间．本文主要结果是：（１）如果（Ｅ，Ｔ）是次可分的，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．（２）如果（Ｅ，Ｔ）是强次可分且（Ｅ，β（Ｅ，Ｅ））是桶型空间，那么ＡＥ是相对弱紧集Ａ是相对弱可数紧集Ａ是相对弱序列紧集．     

Banach空间的弱*序列紧性

本文研究了Ｂａｎａｃｈ空间的弱序列紧性．Ｂａｎａｃｈ空间Ｘ称为有（ｗ）性质，如果Ｘ（Ｘ的共轭空间）的每个有界序列有弱收敛子列．我们证明了，如果Ｂａｎａｃｈ空间Ｘ有（ｗ）性质，那么ｌｐ（Ｘ）（１≤ｐ＜＋∞）与ｃ０（Ｘ）也有（ｗ）性质．     

弱Herz空间的应用

设１〈ｑ〈∞和０〈ｐ≤１，本文证明了一大类算子有界地映Ｈｅｒｚ空间Ｋｑ＾ｎ（１－１／ｑ，＾ｐ（Ｒ＾ｎ）到弱Ｈｅｒｚ空间ＷＫｑ＾ｎ（１－１／ｑ），＾ｐ（Ｒ＾ｎ）。本文还引入了弱Ｈｅｒｚ型Ｈａｒｄｙ空间，并且证明了局部Ｃａｌｄｅｒｏｎ－Ｚｙｇｍｕｎｄ型算子有界地映Ｈｅｒｚ型Ｈａｒｄｙ空间到弱Ｈｅｒｚ型Ｈａｒｄｙ空间。     

Banach空间的弱序列紧性

本文研究了Banach空间的弱*序列紧性，Banach空间X称为有(ω)性质，如果X’（X的共轭空间）的每个有界序列有弱*收敛子列，我们证明了，如果Banach空间X有(ω)性质，那么lp(X)(1≤p＜ ∞)与c0(X)也有(ω)性质。     

紧局部完全ω凸空间

本文引入紧完全ω凸空间（ＣωＲ）和紧局部完全ω凸空间（ＣＬωＲ）概念，得到如下结果：若Ｘ是ＣＬωＲ，则Ｘ有（Ｋ）性质；若Ｘ＾＊是ＣＬωＲ，则Ｘ＾＊有（＊＊）性质。     

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。     

L—不分明拓扑空间的Alexandorff紧化

给出了一般的Ｌ－不分明拓扑空间的Ａｌｅｘａｎｄｏｒｆｆ紧化，并且对弱诱导空间证明了该紧化是弱诱导紧化类中唯一最小的紧化。     

次可分与拟可分的Banach空间

Ｘ是Ｂａｎａｃｈ空间，对Ｘ的每一弱可分且弱紧的子集Ｋ，若（ｋ，ω）可度量，则称Ｘ是次可分的。如果对任意的可分，则称Ｘ是拟可分的。本文证明了这两类新引入的空间比可分空间与弱紧生成的Ｂａｎａｃｈ空间都要广泛并且保留了可分空间的许多重要性质。     

一类局部凸空间及其映照特征

称局部凸空间（E,(?)0）为WCM空间若对于任何弱于(?)0的局部凸拓扑(?),（E,(?)）与（E,(?)0）具相同的弱紧圆凸集.本文研究了WCM空间的存在性及其与其他类型局部凸空间之间的关系,还给出了WCM空间的一种映照特征.     

Relatively Compact Sets on Abstract Wiener Space

In this note, we obtain a sufficient and necessary condition for a set in an abstract Winner space （X, H, μ） to be relatively compact in L^2（X, μ）. Meanwhile, we give a sufficient condition for relative compactness in L^P（X, μ） for p〉1. We also provide an example of Da Prato-Malliavin Nualart to show the result.     

Every weakly compact set can be uniformly embedded into a reflexive Banach space

Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space.     

Banach空间中远达和同时远达问题的适定性

本文研究Ｂａｎａｃｈ空间Ｘ中远达和同时远达问题的适定性,在集合的Ｈａｕｓ－ ｄｏｒｆｆ距离下,对Ｘ中的闭凸子集Ｄ和相对弱紧的有界闭子集Ｋ,证明了下述结果： 若Ｄ关于Ｋ严格凸和有Ｋａｄｅｃ性质,则Ｄ中所有使远达问题 ｍａｘ｛ｘ,Ｋ｝是适定的 点ｘ全体在Ｄ中是Ｇδ型集．作为应用,得到了同时远达问题适定性的类似结果．     

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.     

Strong Minkowski Separation and Co-Drop Property

In the framework of topological vector spaces, we give a characterization of strong Minkowski separation, introduced by Cheng, et al., in terms of convex body separation. From this, several results on strong Minkowski separation are deduced. Using the results, we prove a drop theorem involving weakly countably compact sets in locally convex spaces. Moreover, we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property. If the underlying locally convex space is quasi-complete, then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.     

局部强紧空间的Hoare空间与Smyth空间

本文主要讨论局部强紧空间的性质,特别是其Hoare空间和Smyth空间的性质,证明了T_0空间为局部强紧空间的当且仅当其Hoare空间为局部强紧空间,局部强紧空间的Smyth空间为C-空间.对于强局部紧空间,我们有类似的结论.     

广义共同逼近问题的适定性

设C是实Banach空间X中有界闭凸子集且0是C的内点，G是X中非空闭的有界相对弱紧子集.记K(X)为X的非空紧凸子集全体并赋Hausdorff距离，KG(X)为集合｛A∈K(X)；A∩G=｝的闭包.称广义共同逼近问题minC(A,G)是适定的是指它有唯一解(x0,z0)，且它的每个极小化序列均强收敛到(x0,z0).在C是严格凸和Kadec的假定下，证明了｛A∈K(X)；minC(A，G)是适定的｝含有KG(X)中稠Gδ子集，这本质地推广和延拓了包括De Blasi,Myjak and Papini［1］、Li［2］和De Blasi and Myjak［3］等人在内的近期相应结果.     

Locally Compact Path Spaces

It is shown that the space X^[0,1], of continuous maps [0,1]X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. For a T₁-space X, it follows that X^[0,1] is locally compact if and only if X is locally compact and totally path-disconnected. Mathematics Subject Classifications (2000) 54C35, 54E45, 55P35, 18B30, 18D15.     

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.