k半层空间的性质及相关问题

k半层空间是层空间与N空间的共同推广,本文综述k半层空间的研究进展,介绍k半层空间的刻画、性质及其推广,给出一些相关问题,供进一步研究.     

A normal screenable nonparacompact space in ZFC

We construct a normal, screenable, nonparacompact space in ZFC. The existence of such a space is also known to imply that there is a normal, screenable space which is not collectionwise normal.

     

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.     

LF拟仿紧空间

本文定义了ＬＦ拟仿紧空间的概念，用半内部等概念给出ＬＦ拟仿紧空间的刻划，作者讨论了ＬＦ拟仿紧空间的半正则化，Ｌ－好的推广等问题，得到一系列结果，还在几乎Ｈｕｔｔｏｎ正则ＬＦ拓扑空间中讨论了ＬＦ拟仿紧空间的进一步的性质。     

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.     

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.     

On minimal strongly KC-spaces

In this article we introduce the notion of strongly KC-spaces, that is, those spaces in which countably compact subsets are closed. We find they have good properties. We prove that a space (X, τ) is maximal countably compact if and only if it is minimal strongly KC, and apply this result to study some properties of minimal strongly KC-spaces, some of which are not possessed by minimal KC-spaces. We also give a positive answer to a question proposed by O.T. Alas and R.G. Wilson, who asked whether every countably compact KC-space of cardinality less than c has the FDS-property. Using this we obtain a characterization of Katítov strongly KC-spaces and finally, we generalize one result of Alas and Wilson on Katìtov-KC spaces. This research was supported by NSFC of China (No. 10671173).     

仿紧局部紧空间映象的若干结论的推广

让ψ是蕴含仿紧性的映射保持的闭遗传性质．本文建立了仿紧局部ψ空间的闭映象、某些序列覆盖L映象的内在特征的一般性定理,推广了仿紧局部紧空间映象等的若干结论．