| An Application of Set Theory in Quasi-Paracompactness |
| Received:January 19, 2022 Revised:May 08, 2022 |
| Key Words:
quasi-paracompact space weak continuum hypothesis irreducible space $\omega_1$-compact space Stone-\v{C}ech compactification
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.12171015) and the Natural Science Foundation of Fujian Province (Grant Nos.2020J01428; 2020J05230). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.06.009 |
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