| 描述拓扑空间的几种方法 |
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| 引用本文： | 张晓敏. 描述拓扑空间的几种方法[J]. 安庆师范学院学报(自然科学版), 2012, 18(2): 37-40 |
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| 作者姓名： | 张晓敏 |
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| 作者单位： | 陕西省行政学院,陕西西安,710068 |
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| 摘 要： | 从映射的角度定义了内部运算、邻域系运算、邻域基运算及相应的公理,分别由它们导出了拓扑与拓扑空间,证明了闭集公理、内部公理、邻域基公理与所定义拓扑的三个条件等价,举反例说明了在等价前提下公理条件存在的必要性,最后讨论了导集的一些性质。
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| 关 键 词： | 拓扑 拓扑空间 闭集 内部 邻域系 邻域基 导集 |
Some Ways to Describe Topological Space |
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| ZHANG Xiao-min. Some Ways to Describe Topological Space[J]. Journal of Anqing Teachers College(Natural Science Edition), 2012, 18(2): 37-40 |
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| Authors: | ZHANG Xiao-min |
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| Affiliation: | ZHANG Xiao-min(Shaanxi Administration School,Xi’an,Shaanx 710068,China) |
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| Abstract: | In this paper,we introduce the concepts of interior operator,neighborhood system operator,base for the neighborhood system operator and correspondent axioms from the angle of mapping,then induct topologies and topological spaces.By them,we prove the equivalence between the three conditions of topology and axiom of closed set,axiom of interior,axiom of neighbourhood system,axiom of base for the neighborhood system,and give opposite examples to show the necessities of the conditions in axioms.We also discuss some properties of derived set. |
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| Keywords: | Topelogy topological space closed set interior neighbourhcod system base for the neighborhood system de- rived set |
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