Large regular Lindelöf spaces with points Gδ

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    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.

    元の言語English
    ページ(範囲)249-260
    ページ数12
    ジャーナルFundamenta Mathematicae
    237
    発行部数3
    DOI
    出版物ステータスPublished - 2017

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    ASJC Scopus subject areas

    • Algebra and Number Theory

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