| 集合论在拟仿紧性中的应用 |
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| 引用本文： | 周先耕,林寿. 集合论在拟仿紧性中的应用[J]. 数学研究及应用, 2022, 42(6): 653-657 |
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| 作者姓名： | 周先耕 林寿 |
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| 作者单位： | 宁德师范学院数学研究所, 福建 宁德 352100 |
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| 基金项目： | 国家自然科学基金(Grant No.12171015),福建省自然科学基金(Grant Nos.2020J01428; 2020J05230). |
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| 摘 要： | 1977年,刘应明引进拟仿紧性并证明了下述集论拓扑学的结果：在假设$2^{omega_1}>2^{omega}$下每一个可分正规的拟仿紧空间是仿紧空间.我们进一步证明假设$2^{omega_1}>2^{omega}$等价于每一个可分正规的拟仿紧空间是仿紧空间,获得了拟仿紧性的一个独立性结果.
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| 关 键 词： | 拟仿紧空间；弱连续统假设；不可约空间；$omega_1$紧空间； Stone-image ech 紧化 |
| 收稿时间： | 2022-01-19 |
| 修稿时间： | 2022-05-08 |
An Application of Set Theory in Quasi-Paracompactness |
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| Xiangeng ZHOU,Shou LIN. An Application of Set Theory in Quasi-Paracompactness[J]. Journal of Mathematical Research with Applications, 2022, 42(6): 653-657 |
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| Authors: | Xiangeng ZHOU Shou LIN |
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| Affiliation: | Institute of Mathematics, Ningde Normal University, Fujian 352100, P. R. China |
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| Abstract: | In 1977, Yingming Liu introduced quasi-paracompactness and proved that under $2^{omega_1}>2^{omega}$ every separable normal quasi-paracompact space is a paracompact space, which is a result of set-theoretic topology. In this paper we further prove that hypothesis ``$2^{omega_1}>2^{omega}$'' is equivalent to that every separable normal quasi-paracompact space is a paracompact space, which gives an independent result of quasi-paracompactness. |
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| Keywords: | quasi-paracompact space weak continuum hypothesis irreducible space $omega_1$-compact space Stone-v{C}ech compactification |
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