### Abstract

By analyzing Dow's construction, we introduce a general construction of regular Lindelof spaces with points Gδ. Using this construction, we prove the following: Suppose that either (1) there exists a regular Lindel of P-space of pseudocharacter ≤ ω1 and of size > 2ω, (2) CH and (ω2) hold, or (3) CH holds and there exists a Kurepa tree. Then there exists a regular Lindel of space with points Gδ and of size > 2ω. This shows that, under CH, the non-existence of such a Lindel of space has a large cardinal strength. We also prove that every c.c.c. forcing adding a new real creates a regular Lindel of space with points Gδ and of size at least (2ω1 )V.

Original language | English |
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Pages (from-to) | 249-260 |

Number of pages | 12 |

Journal | Fundamenta Mathematicae |

Volume | 237 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2017 |

### Keywords

- Kurepa tree
- Lindel of space
- P-space
- Points Gδ
- Square principle

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Usuba, T. (2017). Large regular Lindelöf spaces with points Gδ.

*Fundamenta Mathematicae*,*237*(3), 249-260. https://doi.org/10.4064/fm296-8-2016