Large regular Lindelöf spaces with points Gδ

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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 languageEnglish
Pages (from-to)249-260
Number of pages12
JournalFundamenta Mathematicae
Volume237
Issue number3
DOIs
Publication statusPublished - 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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