TY - JOUR

T1 - C⁎-embedding and P-embedding in subspaces of products of ordinals

AU - Kemoto, Nobuyuki

AU - Usuba, Toshimichi

N1 - Funding Information:
This research was supported by Grant-in-Aid for Scientific Research (C) 21K03339.
Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/8/15

Y1 - 2022/8/15

N2 - 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)×ω1 such that the closed subspace X∩({ω}×ω1) is C⁎-embedded in X but not P-embedded in X, • for every subspace X of (ω+1)×ω1, if the closed subspace X∩({ω}×ω1) is C⁎-embedded in X, then it is P-embedded in X.

AB - 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)×ω1 such that the closed subspace X∩({ω}×ω1) is C⁎-embedded in X but not P-embedded in X, • for every subspace X of (ω+1)×ω1, if the closed subspace X∩({ω}×ω1) is C⁎-embedded in X, then it is P-embedded in X.

KW - 2<2

KW - Almost disjoint family

KW - C-embedding

KW - Consistent

KW - Independent family

KW - P-embedding

KW - Subspaces of products of ordinals

UR - http://www.scopus.com/inward/record.url?scp=85134487905&partnerID=8YFLogxK

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U2 - 10.1016/j.topol.2022.108194

DO - 10.1016/j.topol.2022.108194

M3 - Article

AN - SCOPUS:85134487905

VL - 318

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

M1 - 108194

ER -