Compact covering mappings and cofinal families of compact subsets of a Borel set

Volume 167 / 2001

G. Debs, J. Saint Raymond Fundamenta Mathematicae 167 (2001), 213-249 MSC: Primary 03E15; Secondary 03E45, 54H05. DOI: 10.4064/fm167-3-2

Abstract

Among other results we prove that the topological statement “Any compact covering mapping between two ${\bf \Pi }^0_{3}$ spaces is inductively perfect” is equivalent to the set-theoretical statement “$\forall \alpha \in \omega ^\omega ,$ $\omega _1^{L(\alpha )}<\omega _1$”; and that the statement “Any compact covering mapping between two coanalytic spaces is inductively perfect” is equivalent to “Analytic Determinacy”. We also prove that these statements are connected to some regularity properties of coanalytic cofinal sets in ${\cal K}(X)$, the hyperspace of all compact subsets of a Borel set $X$.

Authors

  • G. DebsEquipe d'Analyse
    Université Paris 6
    Boîte 186
    4, place Jussieu
    75252 Paris CEDEX 05, France
    e-mail
  • J. Saint RaymondEquipe d'Analyse
    Université Paris 6
    Boite 186
    4, place Jussieu
    75252 Paris CEDEX 05, France
    e-mail

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