Large regular Lindelöf spaces with points Gδ

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    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

    Fingerprint

    Pseudocharacter
    Lindelöf Space
    Large Cardinals
    P-space
    Forcing
    Nonexistence

    Keywords

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

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Large regular Lindelöf spaces with points Gδ. / Usuba, Toshimichi.

    In: Fundamenta Mathematicae, Vol. 237, No. 3, 2017, p. 249-260.

    Research output: Contribution to journalArticle

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