| 对偶导集及其应用 |
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| 引用本文： | 吴洪博,王昭海.对偶导集及其应用[J].数学的实践与认识,2010,40(20). |
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| 作者姓名： | 吴洪博 王昭海 |
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| 基金项目： | 国家自然科学基金，陕西师范大学重点科研基金 |
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| 摘 要： | 借助对偶范畴的思想和方法在点集拓扑学中引入了对偶导集概念,讨论了对偶导集和对偶导集运算的相关性质.并以此为基础引入了对偶连通空间的概念,讨论了对偶连通空间和连通空间之间的关系,借此给出了不连通空间的几个等价刻画.为拓扑空间的研究提供了新的途径.
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| 关 键 词： | 拓扑学 对偶导集 对偶导集运算 对偶连通空间 连通空间 |
The Dual Derived Sets with Its Application |
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| WU Hong-bo,WANG Zhao-hai.The Dual Derived Sets with Its Application[J].Mathematics in Practice and Theory,2010,40(20). |
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| Authors: | WU Hong-bo WANG Zhao-hai |
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| Abstract: | With the help of thoughts and method of dual category,the concept of dual derived set is introduced in point set topology,and the relevant properties of dual derived sets with its algorithm has been discussed.Moreover,based on above results,the concept of dual connected spaces is proposed,and its fundamental properties are studied.Furthermore, several equivalent characterizations of disconnected space are given by using the relation between dual disconnected space and disconnected space. |
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| Keywords: | topology dual derived set operation dual connected space connected space |
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