A characterization of the countable paracompactness for products of ordinals
A characterization of the countable paracompactness for products of ordinals
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序数乘积的可数拟紧性的表征
DOI：
10.1016/j.topol.2020.107325
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发表时间：
2020
影响因子：
0.6
通讯作者：
Yasushi Hirata and Yukinobu Yajima
中科院分区：
文献类型：
--
作者：
Hirata Yasushi;Usuba Toshimichi;Yajima Yukinobu;Yasushi Hirata and Yukinobu Yajima
设A和B是一个序数的两个子空间。证明了乘积A× B是可数仿紧的当且仅当对A× B中的每个正则不可数基数κ和每个闭矩形A′× B′，A′或B′中的任一个包含大小为κ的闭离散子集，只要A′× B′也包含大小为κ的闭离散子集.这个序数的可数仿紧积的刻画比1992年给出的前一个刻画简单得多。
Let A and B be two subspaces of an ordinal. It is proved that the product A× B is countably paracompact if and only if for every regular uncountable cardinal κ and for every closed rectangle A′× B′ in A× B, either A′ or B′ contains a closed discrete subset of size κ whenever so does A′× B′. This characterization of the countably paracompact products of ordinals is much simpler than the previous one given in 1992.