可数生成空间 目录 定义 例子 参见 参考文献 外部链接 导航菜单I-Continuity in Topological SpacesISSN 0001-5962原始内容编辑与修订

点集拓扑学


数学可数序列空间Fréchet空间拓扑空间商不交并拓扑空间范畴余反射子范畴子空间Arens-Fort空间




在数学中，若X 的拓扑由可数集决定，决定方式与收敛序列决定序列空间或Fréchet空间拓扑的方式相同，则称拓扑空间X 是可数生成的（countably generated）。


可数生成空间准确地说是具有可数胎紧性的空间，因此也可以形容为可数胎紧的。




目录





  • 1 定义


  • 2 例子


  • 3 参见


  • 4 参考文献


  • 5 外部链接




定义


若无论何时对於X 中的每一可数子空间U 都有集合V∩Udisplaystyle Vcap U是U 中的闭集，那么V 是X 中的闭集，则拓扑空间X 被称为可数生成的。同样地，X 是可数生成的当且仅当X 的任何子集A 的闭包等於A的所有可数子集的闭包的并。


可数生成空间的商同样是可数生成的。类似地，可数生成空间的不交并也是可数生成的。因此可数生成空间形成了拓扑空间范畴的余反射子范畴，是所有可数空间的余反射包（hull）。


可数生成空间的任何子空间都是可数生成的。



例子


每一序列空间（特别是每一可度量化空间）都是可数生成的。


是可数生成空间但不是序列空间的空间也存在，例如Arens-Fort空间的子空间。



参见



  • 有限生成空间的概念与这一概念有关。


参考文献



  • Herrlich, Horst. Topologische Reflexionen und Coreflexionen. Lecture Notes in Math. 78. Berlin: Springer. 1968. 


外部链接


  • A Glossary of Definitions from General Topology [1]


  • Martin Sleziak. I-Continuity in Topological Spaces (PDF). Acta Mathematica. 2003: 第115－122页. ISSN 0001-5962. （原始内容 (PDF)存档于2004-09-17）. 


KleinBottle-01.png  可数生成空间是一个关于拓扑学的小作品。你可以通过编辑与修订扩充其内容。







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