| 纤维拓扑超空间的局部紧性 |
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| 引用本文： | 韩国涛,;宋玉靖,;李家根. 纤维拓扑超空间的局部紧性[J]. 辽宁师范大学学报(自然科学版), 2014, 0(3): 320-324 |
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| 作者姓名： | 韩国涛, 宋玉靖, 李家根 |
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| 作者单位： | [1]辽宁农业职业技术学院信息工程系,辽宁营口115009; [2]辽宁师范大学数学学院,辽宁大连116029; [3]大连市第二中学数学教研室,辽宁大连116013 |
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| 摘 要： | 纤维拓扑与超空间拓扑,无论在理论上还是在应用中都是有意义的拓扑结构,两个研究领域都产生了丰富的成果.但是迄今为止,探讨复合两种结构的工作还基本没有出现.引入纤维超空间概念,并讨论纤维投射的基本性质.根据该复合结构的特点,定义了纤维超空间的局部紧以及纤维超空间具有局部紧纤维的概念,并讨论了两者间的关系,以及与基底空间相关性质的联系.得到了某些关于紧子集超空间和闭子集超空间纤维紧性,以及纤维超空间局部紧性的一些等价刻画.
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| 关 键 词： | 纤维空间 超空间 有限拓扑 纤维局部紧 |
On local compactness of fibrewise superspace |
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| HAN Guotao;SONG Yujing;LI Jiagen. On local compactness of fibrewise superspace[J]. Journal of Liaoning Normal University(Natural Science Edition), 2014, 0(3): 320-324 |
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| Authors: | HAN Guotao SONG Yujing LI Jiagen |
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| Affiliation: | HAN Guotao , SONG Yujing , LI Jiagen ( 1. Department of Information Engineering, Liaoning Agriculture Vacation-Technical College, Yingkou 115009, China ; 2. School of Mathematics, Liaoning Normal University, Dalian 116029, China; 3. Department of Mathematics, Dalian No. 2 Senior High School,Dalian 116013,China) |
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| Abstract: | Fibrewise topology and superspace topology are two meaningful topological structures both in theory and application,and there are rich research achievements in both fields. So far, however, there is little research work to compound the two structures. The paper poses the nation of fibrewise superspace,and discusses the basic properties of fibrewise function. It also defines the local compactness of fibrewise superspace and the fibrewise superspace with local compact fibre,and discusses the relations between the two properties. The equivalence conditions for fiberwise compactness of superspace of compact subsets and superspace of colsed subsets, and the equivalent conditions of local compactness of fibrewise superspace are obtained in this paper. |
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| Keywords: | fibrewise space superspace finite topology fibrewise local compactness |
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