| 内超实度量空间中的两种收敛性 |
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| 引用本文： | 张福泰.内超实度量空间中的两种收敛性[J].陕西师范大学学报,1998(3). |
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| 作者姓名： | 张福泰 |
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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： | 用无穷小分析方法研究了内超实度量空间中与Ｑ－拓扑及Ｓ－拓扑相应的两种收敛性——Ｑ－收敛性及Ｓ－收敛性，给出了内超实度量空间中的点列、网以及函数列Ｑ－收敛与Ｓ－收敛的特征与基本性质，引进了一致Ｑ－收敛与一致Ｓ－收敛的概念，并讨论了这些收敛性在一般度量空间中的应用．
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| 关 键 词： | 内超实度量空间 Q－收敛 S－收敛 k－饱和原理 惯性原理 |
Two kinds of convergence in an internal hyperreal metric space |
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| Zhang Futai.Two kinds of convergence in an internal hyperreal metric space[J].Journal of Shaanxi Normal University: Nat Sci Ed,1998(3). |
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| Authors: | Zhang Futai |
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| Abstract: | The methods of infinitesimal analysis are used to study two kinds of convergence, i.e. Q convergence and S convergence corresponding to Q topology and S topology in an internal hyperreal metric space. Several basic properties of Q convergent or S convergent sequences, nets, and sequences of functions are proved. The concepts of uniform Q convergence and uniform S convergence are introduced. Some applications of these kinds of convergence in general metric spaces are also discussed |
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| Keywords: | internal hyperreal metric space Q convergence S convergence k saturation principle permanence principle |
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