| 超实数域^＊R的拓扑结构 |
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| 引用本文： | 张福泰,冯汉桥.超实数域^＊R的拓扑结构[J].数学进展,1997,26(5):435-439. |
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| 作者姓名： | 张福泰 冯汉桥 |
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| 作者单位： | 陕西师范大学计算机科学系 |
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| 摘 要： | 研究了超实数域上两种有用的拓扑－Ｑ－拓扑和Ｓ－拓扑。证明了以下结果：空间（＊Ｒ，Ｑ）是完全不连通的；＾＊Ｒ的Ｑ－紧子集只有有限集；＾＊Ｒ中的每一个银河是（＊Ｒ，Ｓ）的一个连通分支；＾＊Ｒ中的每一个具有有限长度的区间（不必是闭的）都是Ｓ－紧的，同时也纠正了《Ｍａｔｈ．Ｊａｐｏｎｉｃａ》上一篇论文中关于＾＊Ｒ上的Ｑ－拓扑的性质的一些错误。
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| 关 键 词： | 超实数域 Q－拓扑 S－拓扑 可数概括原理 拓扑结构 |
The Topological Structures of the Hyperreal Number Field *R |
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| Zhang Futai,Feng Hanqiao.The Topological Structures of the Hyperreal Number Field *R[J].Advances in Mathematics,1997,26(5):435-439. |
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| Authors: | Zhang Futai Feng Hanqiao |
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| Abstract: | Two kinds of useful topologies, i.e. Q -topology and S -topology on the field of hyperreal numbers are studied. The following results are proved: The space ( tR, Q) is totally disconnected; only finite subsets of * R are Q -compact; Every galaxy of * R is a connected component of ( * R, S) ; Every interval in * R (not necessarily closed) with finite length is S -compact. Some mistakes about the properties of Q -topology in another paper on Math. Japonica are corrected as well. |
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| Keywords: | hyperreal number field Q -topology S -topology standard part mapping countably comprehensive principle |
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