## Abstract

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.

Original language | English |
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Article number | 108194 |

Journal | Topology and its Applications |

Volume | 318 |

DOIs | |

Publication status | Published - 2022 Aug 15 |

## Keywords

- 2<2
- Almost disjoint family
- C-embedding
- Consistent
- Independent family
- P-embedding
- Subspaces of products of ordinals

## ASJC Scopus subject areas

- Geometry and Topology

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