Abstract
AbstractGiven a compact Polish space E and the hyperspace of its compact subsets ${\cal K}\left( E \right)$, we consider Gδ σ-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.
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