两个序数子集的乘积空间的β-正规性(英文)

β-normality in Products of Two Ordinals

设k为不可数序数,其上拓扑为序拓扑.A和B为k的任何子空间.本文证明了对乘积空间A×B.正规性、集体正规性、收缩性和β-正规性都是等价的.

Let A and B be subspaces of the initial segment of an uncountable ordinal number κ with the order topology. In this paper, we prove that for the product A × B, the properties of normality, collectionwise normality, shrinking property and β-normality are all equivalent.