| 关于可数中紧空间的映射定理 |
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| 引用本文： | 王秋利,燕鹏飞.关于可数中紧空间的映射定理[J].五邑大学学报(自然科学版),2012,26(2):5-7. |
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| 作者姓名： | 王秋利 燕鹏飞 |
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| 作者单位： | 五邑大学数学与计算科学学院,广东江门,529020 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 通过可数中紧空间的等价刻画给出了关于可数中紧性的几个映射定理：1）可数中紧性在闭的紧覆盖映射下是保持的;2）可数中紧的Frechet空间在闭映射下的像是可数中紧的;3）可数中紧性的拟完全原象是可数中紧的;4）可数中紧空间与紧空间的积空间是可数中紧的.
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| 关 键 词： | 可数中紧空间 紧覆盖映射 闭映射 拟完全映射 |
Mapping Theorems on Countably Mesocompact Spaces |
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| WANG Qiu-li,YAN Peng-fei.Mapping Theorems on Countably Mesocompact Spaces[J].Journal of Wuyi University(Natural Science Edition),2012,26(2):5-7. |
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| Authors: | WANG Qiu-li YAN Peng-fei |
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| Institution: | (School of Mathematics and Computation Science,Wuyi University,Jiangmen 529020,China) |
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| Abstract: | Several mapping theorems on countably mesocompact spaces are given through equivalent characterizations: 1) Countably mesocompactness is preserved under closed and compact-covering mappings;2) The image of a countably mesocompact and Frechet space under a closed mapping is countably mesocompact;3) The original image of a countably mesocompact space under a quasi-perfect mappings is countably mesocompact;4) If is a countably mesocompact space and is a compact space,then is also a countably mesocompact space. |
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| Keywords: | countably mesocompact spaces compact-covering mapping closed mapping quasiperfect mapping |
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