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2 results

  • Gδ Sets IN σ-IDEALS GENERATED BY COMPACT SETS

  • MAYA SARAN
  • Journal:
    The Journal of Symbolic Logic / Volume 84 / Issue 2 / June 2019
    Published online by Cambridge University Press:
    04 March 2019, pp. 781-797
    Print publication:
    June 2019

  • Given a compact Polish space E and the hyperspace of its compact subsets ${\cal K}\left( E \right)$, we consider Gδσ-ideals of compact subsets of E. Solecki has shown that any σ-ideal in a broad natural class of Gδ ideals can be represented via a compact subset of ${\cal K}\left( E \right)$; in this article we examine the behaviour of Gδ subsets of E with respect to the representing set. Given an ideal I in this class, we construct a representing set that recognises a compact subset of E as being “small” precisely when it is in I, and recognises a Gδ subset of E as being “small” precisely when it is covered by countably many compact sets from I.