双预拓扑空间的连通类  

Connectednesses of bi-pre-topological spaces

作　　者：李生刚[1] 申文霞[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《纺织高校基础科学学报》2012年第1期1-4,共4页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金资助项目(11071151)

摘　　要：运用拓扑和范畴论方法研究了双预拓扑空间的连通类,给出了双预拓扑空间连通类的等价刻画.证明了双预拓扑空间范畴是topological construct、最小双预拓扑空间连通类和最大双预拓扑空间连通类是存在的、双预拓扑空间连通类是连续闭的、一族双预拓扑空间连通类的交是双预拓扑空间连通类.并且建立了预拓扑空间连通类与双预拓扑空间连通类的密切联系.Connectednesses of bi-pre-topological spaces are studied by using topological and categorial methods. A characterization of connectednesses of bi-pre-topological spaces is given. It is proved that the category of bi-pre-to- pological spaces and continuous mappings between them is a topological construct, the smallest connectedness and the biggest connectedness of bi-pre-topological spaces exist, every connectedness of bi-pre-topological spaces is a continuously dosed class, and the intersection of a family of connectednesses of bi-pre-topological spaces is still a connectednesses. Moreover, close connections between connectednesses of pre-topological spaces and connected- nesses of bi-pre-topological spaces are established.

关 键 词：双预拓扑空间I连通类l范畴 toDoloeical CONSTRUCT 

分 类 号：O189.1[理学—数学]