集合论在拟仿紧性中的应用

An Application of Set Theory in Quasi-Paracompactness

中文关键词:  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

英文关键词:quasi-paracompact space  weak continuum hypothesis  irreducible space  $\omega_1$-compact space  Stone-\v{C}ech compactification

中文摘要:

      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.

英文摘要:

      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.