| 双预拓扑空间的连通类 |
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| 引用本文： | 李生刚,申文霞. 双预拓扑空间的连通类[J]. 纺织高校基础科学学报, 2012, 25(1): 1-4 |
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| 作者姓名： | 李生刚 申文霞 |
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| 作者单位： | 陕西师范大学 数学与信息科学学院,陕西西安,710062 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 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．
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| 关 键 词： | 双预拓扑空间I连通类l范畴 toDoloeical construct |
Connectednesses of bi-pre-topological spaces |
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| LI Sheng-gang , SHEN Wen-xia. Connectednesses of bi-pre-topological spaces[J]. Basic Sciences Journal of Textile Universities, 2012, 25(1): 1-4 |
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| Authors: | LI Sheng-gang SHEN Wen-xia |
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| Affiliation: | (College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China) |
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| Abstract: | 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-topological 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 closed 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 connectednesses of bi-pre-topological spaces are established. |
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| Keywords: | bi-pre-topological space connectednesses category topological construct |
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