| 拓扑空间中的三个典型反例 |
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| 引用本文： | 艾素梅.拓扑空间中的三个典型反例[J].沧州师专学报,2009,25(4):97-98. |
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| 作者姓名： | 艾素梅 |
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| 作者单位： | 沧州师范专科学校,数学系,河北,沧州,061001 |
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| 摘 要： | 拓扑空间中的反例,在学习和研究拓扑学理论中起着重要的作用,一个好的反例可以为拓扑理论找出存在的依据。这里给出三个反例,存在两个度量空间X与Y,使X2与Y2等距而X与Y并不等距是拓扑空间中的反例;存在不可度量化的紧的完全正规空间是拓扑空间分离性的反例;不存在非零连续线性泛函的线性拓扑空间是线性拓扑空间的反例。
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| 关 键 词： | 拓扑空间 反例 线性拓扑 |
Three Typical Counter-examples in the Topological Space |
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| AI Su-mei.Three Typical Counter-examples in the Topological Space[J].Journal of Cangzhou Teachers‘College,2009,25(4):97-98. |
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| Authors: | AI Su-mei |
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| Institution: | AI Su-mei(Mathematics Department,Cangzhou Teachers' College,Cangzhou,061001,Hebei) |
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| Abstract: | Counter-examples in the topological space play an important role in the topology learning and research.A good counter-example can find out the basis for the existence of topological theory.Three counter-examples of topological space are proposed in this study: There are two metric spaces,X and Y,in which and are isometric,whileand are not isometric;Non-metric tight regular space is a counter-example of the separation of topological space;No non-zero continuous linear functionals of the linear topological sp... |
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| Keywords: | topological space counter-example linear topology |
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