| 粗拓扑空间的Higson紧化 |
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| 引用本文： | 王勤,张艳梅. 粗拓扑空间的Higson紧化[J]. 复旦学报(自然科学版), 2004, 43(3): 379-385 |
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| 作者姓名： | 王勤 张艳梅 |
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| 作者单位： | 复旦大学,物理系,上海,200433;东华大学,应用数学系,上海,200051;复旦大学,数学研究所,上海,200433 |
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| 摘 要： | 研究局部紧Hausdorff空间X的Proper粗结构及其相应的Higson紧化，并证明X的Stone-Cech紧化和一点紧化分别是X关于紧子集粗结构和Proper粗结构的Higson紧化．同时研究Higson紧化在粗拓扑空间范畴的函子性质，并用这种函子性质刻画了Higson紧化的逆极限．特别地，证明了Stone-Cech紧化是某些Higson紧化的逆极限．
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| 关 键 词： | Higson紧化 粗拓扑空间 逆极限 Stone-ech紧化 |
Higson Compactifications of CoarseTopological Spaces |
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| Abstract. Higson Compactifications of CoarseTopological Spaces[J]. Journal of Fudan University(Natural Science), 2004, 43(3): 379-385 |
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| Authors: | Abstract |
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| Abstract: | Higson compactifications of a locally compact Hausdorff space X associated with proper coarse structures are studied. It shows that both the Stone-ech compactification and the one-point compactification of X are certain Higson compactifications. It is also proved that Higson compactification is a functor on the category of coarse topological spaces and continuous coarse mappings. As a result, the Stone-ech compactification of X can be represented as an inverse limit of Higson compactifications. |
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| Keywords: | Higson compactification coarse topological space inverse limit Stone-ech compactification |
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