Abstract
Let A and B be subspaces of the initial segment of an uncountable ordinal number κ with the order topology. We prove: 1. (i) For the product A × B, the following properties (1)-(3) are equivalent: (1) shrinking property; (2) collectionwise normality; and (3) normality. 2. (ii)For the product A × B, the following properties (4)-(7) are equivalent: (4) strong D- property; (5) expandability; (6) countable paracompactness; and (7) weak D(ω)-property. 3. (iii) If κ = ω 1, then for A × B, the properties (1)-(7) above are equivalent, and A × B has one of them iff A or B is not stationary, or A ∩ B is stationary. 4. (iv) If κ is regular and A and B are stationary, then A × Bis κ-compact iff A ∩ B is stationary.
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