On <Emphasis Type="Italic">k</Emphasis>-Spaces and <Emphasis Type="Italic">k</Emphasis><Subscript><Emphasis Type="Italic">R</Emphasis></Subscript>-Spaces

In this note we study the relation between k _R -spaces and k-spaces and prove that a k _R -space with a σ-hereditarily closure-preserving k-network consisting of compact subsets is a k-space, and that a k _R -space with a point-countable k-network consisting of compact subsets need not be a k-space. This work was supported by the NSF of China (10271056).     

k-systems, k-networks and k-covers

The concepts of k-systems, k-networks and k-covers were defined by A. Arhangel’skii in 1964, P. O’Meara in 1971 and R. McCoy, I. Ntantu in 1985, respectively. In this paper the relationships among k-systems, k-networks and k-covers are further discussed and are established by mk-systems. As applications, some new characterizations of quotients or closed images of locally compact metric spaces are given by means of mk-systems.     

On weak bases

In this paper, we give an affirmative answer to Tanaka's question: Is a space X with a σ-hereditarily closure-preserving weak base g-metrizable? [Proc. Aroc. Amer. Math. Soc. 112 (1991) 283] and a negative answer to S. Lin's question: Is every weak base of a topological space a k-network? [S. Lin, Generalized Metric Spaces and Maps, Science Press, 1995, Problem 1.6.20]. We also discuss mapping theorems on weak bases and the product of weak bases.     

具有σ遗传闭包保持双网的空间

证明了正则空间X具有σ遗传闭包保持双网当且仅当或X是cosmic空间，或X是σ闭离散空间，回答了[1]提出的一个问题．     

仿紧映射及亚紧映射

主要利用开覆盖的局部有限,点有限半开加细及内核保持定向开覆盖的闭包保持闭加细,内核保持开星加细等进一步刻划仿紧映射和亚紧映射.     

弱基与覆盖性质

本文证明了具有σ闭包保持弱基的正则空间是遗传亚Lindelof空间，由此获得了g可度量空间的一个等价刻画。     

强∑~*空间是D空间

研究了强Σ~*空间和D空间的关系,证明了强Σ~*空间是D空间,改进了R.Z.Buzyakova等的结果.     

关于（mod K）可度量空间

本文的主要结果是证明在Ｔ１空间类中下列条件相互等价：（１）空间具有σ局部有限（ｍｏｄ Ｋ）基。（２）空间具有σ遗传闭包保持（ｍｏｄ Ｋ）基。（３）空间具有σ紧有限（ｍｏｄ Ｋ）基。