C*-embedding and P-embedding in subspaces of products of ordinals
C*-embedding and P-embedding in subspaces of products of ordinals
复制标题
序数乘积子空间中的 C* 嵌入和 P 嵌入
DOI：
10.1016/j.topol.2022.108194
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发表时间：
2022
影响因子：
0.6
通讯作者：
Toshimichi Usuba
中科院分区：
文献类型：
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作者：
Nobuyuki Kemoto;Toshimichi Usuba
已知在X= A× B中，A和B是序数的子空间，X的所有闭C-嵌入子空间都是P-嵌入的.还问是否所有封闭的C-嵌入子空间的X是P-嵌入的，只要X是一个子空间的产品的两个序数。在本文中，我们证明了以下两个与ZFC一致：·存在（ω+ 1）× ω 1的子空间X，使得闭子空间X∩（{ω}× ω 1）是C-嵌入在X中，但不是P-嵌入在X中，·对于（ω+ 1）× ω 1的每个子空间X，如果闭子空间X∩（{ω}× ω 1）是C-嵌入在X中，那么它是P-嵌入在X中。
It is known that in X= A× B, where A and B are subspaces of ordinals, all closed C⁎-embedded subspaces of X are P-embedded. Also it is asked whether all closed C⁎-embedded subspaces of X are P-embedded whenever X is a subspace of products of two ordinals. In this paper, we prove that both of the following are consistent with ZFC:• there is a subspace X of (ω+ 1)× ω 1 such that the closed subspace X∩({ω}× ω 1) is C⁎-embedded in X but not P-embedded in X,• for every subspace X of (ω+ 1)× ω 1, if the closed subspace X∩({ω}× ω 1) is C⁎-embedded in X, then it is P-embedded in X.