| 对近似收敛数列空间A_c(R)性质的探讨 |
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| 引用本文： | 郭佩佩,罗成.对近似收敛数列空间A_c(R)性质的探讨[J].内蒙古大学学报(自然科学版),2011,42(2):146-152. |
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| 作者姓名： | 郭佩佩 罗成 |
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| 作者单位： | 内蒙古大学数学科学学院,呼和浩特,010021 |
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| 基金项目： | 内蒙古自然科学基金项目(批准号:200208020105);内蒙古自然科学基金项目(批准号:200308020101) |
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| 摘 要： | 从实数域上近似收敛数列空间Ac(R)定义出发,指出了收敛数列空间和近似收敛数列空间Ac(R)的包含关系和稠密性,介绍了近似收敛数列空间Ac(R)的一些基本性质,着重讨论了近似收敛数列空间Ac(R)的可分性及其对偶空间,最后又给出了近似收敛数列空间Ac(R)不是局部凸且不是局部有界的证明.
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| 关 键 词： | 近似收敛 对偶 可分 局部凸 局部有界 |
A Study for the Properties of the Approximate Convergent Sequence Space |
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| GUO Pei-pei,LUO Cheng.A Study for the Properties of the Approximate Convergent Sequence Space[J].Acta Scientiarum Naturalium Universitatis Neimongol,2011,42(2):146-152. |
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| Authors: | GUO Pei-pei LUO Cheng |
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| Institution: | GUO Pei-pei,LUO Cheng(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China) |
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| Abstract: | Based on the definition of approximate convergent sequence space Ac(R),the denseness and the inclusion relationship between the convergent sequence space and approximate convergent sequence space Ac(R) are pointed out.Some basic properties of approximate convergent sequence space Ac(R) are introduced,and the separability of the space Ac(R) and its dual space are discussed.It is proved that approximate convergence sequence space Ac(R) is neither locally convex nor locally bounded. |
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| Keywords: | approximate convergence duality separable locally convex locally bounded |
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