正规可数仿紧空间的逆极限

得到了如下结果:设X是逆系统{Xα,παβ,Λ}的逆极限,|Λ|=λ,假设每个映射πα∶X→Xα是开的且到上的,X是λ-仿紧,每个Xα是正规可数仿紧的,则X是正规可数仿紧的.进一步得到了关于遗传正规且遗传可数仿紧空间的类似结果.     

Strong paracompactness and w- -refinability of inverse limits

In this paper we construct inverse systems of which each space is strongly paracompact and each bonding map and each projection are open and onto maps, and the limit space is paracompact and not strongly paracompact and we investigate -refinability-like properties of limit spaces of inverse systems.

     

关于单调亚紧空间

In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fó-subspaces. For a generalized ordered (GO)-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X* is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.     

关于纤维一般拓扑的一点注记(英文)

Some characterizations of paracompact maps are given in this note, and some equivalent statements of collectionwise normal maps are discussed. And also we show that if f ： X→Y is a closed collectionwise normal map, and f^-1（y） is a semistratifiable subspace of X for any y ∈ Y, then f is a paracompact map.     

Base-cover paracompactness

Call a topological space base-cover paracompact if has an open base such that every cover of contains a locally finite subcover. A subspace of the Sorgenfrey line is base-cover paracompact if and only if it is . The countable sequential fan is not base-cover paracompact. A paracompact space is locally compact if and only if its product with every compact space is base-cover paracompact.

     

Notes on certain quotient images of paracompact locally compact spaces

We continue to study the characterizations of paracompact locally compact spaces under certain quotient mappings, and discuss the relationships among them, which expand the results on certain quotient images of paracompact locally compact spaces. This revised version was published online in June 2006 with corrections to the Cover Date.     

Completely regular paracompact reflection of locales

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.     

k-COVERS AND CERTAIN QUOTIENT IMAGES OF PARACOMPACT LOCALLY COMPACT SPACES

We continue to discuss some properties of certain k-covers. As applications, we give some characterizations of certain quotient images of paracompact locally compact spaces.     

遗传中紧空间与散射分解

本文证明了可数仿紧(中紧、亚紧)空间有类似Junnila的刻画，遗传中紧空间不具有类似Junnila的刻画，并给出了每个散射分解有紧有限的开膨胀的充要条件．     

关于仿紧空间的原象

本文利用ασ仿紧子集的概念,给出了在正则空间条件下,仿紧空间在连续闭映射下的原象是仿紧空间的一个充分条件．这一结果,统一推广了高国士教授与陈必胜教授在两篇论文中的结果．     

Generalized Quasi—Variational Inequalities on Paracompact Sets

Ｔｈｉｓｐａｐｅｒｉｓｃｏｎｔｉｎｕａｔｉｏｎｓｏｆ［１］，ｗｅｓｔｉｌｌｔｏｕｓｅｍａｒｋｓａｎｄｔｅｒｍｓｉｎ［１］ａｎｄｔｈｅｏｔｈｅｒｔｅｒｍｓａｇｒｅｅｗｉｔｈ［２］ａｎｄ［３］．ＬｅｔＥａｎｄＦｂｅｔｗｏＨａｕｓｄｏｒｆｆｔｏｐｏｌｏｇｉｃａｌｖｅｃｔｏｒｓｐａｃｅｓ，ＸＥ，ＹＦｂｅｔｗｏｎｏｎｅｍｐｔｙｓｅｔｓ，ＦｂｅｔｈｅｄｕａｌｓｐａｃｅｏｆＦ，Ａ：Ｘ→２ＹａｎｄＢ：Ｙ→２Ｆｂｅｔｗｏｓｅｔ－ｖａｌｕｅｄｍａｐｐｉｎｇ，Ｔ：Ｙ→Ｘｂｅｉｎｖｅｒｔｉｂｌｅ．Ｉｎｔｈｉｓｐ…     

仿紧集上的拟—似变分不等式

借助于文（１）中的结论研究了仿紧集上的拟－似变分不等式，统一和发展了文（２－６）中的相应结果。     

Shrinking property in Σ-products of paracompact p-spaces

It is shown that a Σ-product of paracompact p-spaces with countable tightness has the shrinking property.     

关于完全仿紧空间的一些刻画

本文在Ｔ１正则的条件下得到了完全仿紧空间的一些等价刻画,并利用所得到的刻画证明了这类空间的一个可数乘积定理。     

仿紧局部可分空间及其映象

探讨仿紧局部可分空间的一些性质,获得了两个可度量化定理,建立了仿紧局部可分空间的各类序列覆盖L-映象的特征。     

仿紧局部cosmic空间的一些性质

给出仿紧局部cosmic空间的一些特征,建立了仿紧局部cosmic空间的几类序列覆盖L映象的特征,证明了闭L映射和商ss映射保持仿紧局部cosmic空间的性质,此外,还给出仿紧局部cosmic空间的一些映射性质。     

Monotone normality and paracompactness

In this paper it is proved that a topological space is necessarily paracompact if it is monotonically normal and any one of the following: screenable, paralindelöf, has a G_δ-diagonal or a quasi-G_δ-diagonal or has a σ-locally-countable base.     

S-paracompact spaces

Summary We introduce the class of S-paracompact spaces as a generalization of paracompact spaces. A space (X,T) is S-paracompact if every open cover of X has a locally finite semi-open refinement. We characterize S-paracompact spaces and study their basic properties. The relationships between S-paracompact spaces and other well-known spaces are investigated.     

Linearly ordered covers,normality and paracompactness

It is shown that a regular space is collectionwise normal and countably paracompact if every open cover has an open, order cushioned refinement. A sufficient condition for paracompactness, in terms of certain order locally finite covers, is given, and is applied to the problem of the paracompactness of product spaces.     

Relative star normal type

In their study of relative metric spaces, Arkhangel'skiĭ and Gordienko introduce several relative properties of paracompactness type. We investigate the relationships between these properties and other relative properties of paracompactness type and answer two questions raised by Arkhangel'skiĭ and Gordienko.

TheoremIf Y is strongly regular in X and 3 paracompact in X then Y is star normal in X.

TheoremY is strongly star normal in X if and only if Y is Aull paracompact in X.

CorollaryIf Y is strongly star normal in X then Y is 2-paracompact in X.

CorollaryIf Y is properly metrizable in X then Y is strongly star normal in X.