| L-拓扑空间的R-强连通性 |
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| 引用本文： | 王小霞,李生刚,伏文清. L-拓扑空间的R-强连通性[J]. 西北纺织工学院学报, 2010, 0(2): 250-253 |
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| 作者姓名： | 王小霞 李生刚 伏文清 |
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| 作者单位： | [1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]延安大学数学与计算机学院,陕西延安716000 |
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| 基金项目： | 国家自然科学基金资助项目（10871121） |
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| 摘 要： | 研究L-拓扑空间中的R-强连通性,运用类比、推广的方法,将一般拓扑空间中的R-强连通性引入到L-拓扑空间中.定义了L-拓扑空间中R-强连通集以及R-强连通L-拓扑空间的概念,证明了L-拓扑空间的R-强连通性具有任意可积性,以及R-强连通性的樊畿定理,得出了R-强连通性是拓扑不变性和L-好的推广等结论.扩展了一般拓扑学中的一些结果.
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| 关 键 词： | L-拓扑空间 R-强连通性 拓扑不变性 L-好的推广 |
R-strong connectedness in L-topological space |
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| WANG Xiao-xia,LI Sheng-gang,FU Wen-qing. R-strong connectedness in L-topological space[J]. Journal of Northwest Institute of Textile Science and Technology, 2010, 0(2): 250-253 |
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| Authors: | WANG Xiao-xia LI Sheng-gang FU Wen-qing |
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| Affiliation: | 1.College of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710062,China;2.College of Mathematics and Computer Science,Yan′an University,Yan′an,Shaanxi 716000,China) |
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| Abstract: | The R-strong connectedness in L-topological spaces was studied.The R-strong connectedness in general topological spaces is introduced to L-topological spaces with the help of methods of analogy and generalization.Concepts of R-strong connected set in L-topological spaces and R-strong connected L-topological spaces are difined.It is proved that R-connected L-topological spaces must be connected and the product of a class of R-strong connected L-topological spaces is also R-strong connected.Then,some characteristics of Rstrong connectedness of L-topological spaces are given,and the Ky Fan theorem of R-strong connectedness is proved.Conclusions that R-strong connectedness of L-topological spaces is a topologically invariant property and an L-good extension of R-strong connectedness of general topological spaces are got.Some results of general topology are extended. |
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| Keywords: | L-topological space R-strong connectedness topologically invariant property Lgood extension |
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