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中文摘要：
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．证明了双预拓扑空闻范畴是topologicalconstruct、最小双预拓扑空阊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．
英文摘要：
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.
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