Maya Saran | Searcharxiv

arXiv2019

$G_δ$ sets in $σ$-ideals generated by compact sets

Given a compact Polish space $E$ and the hyperspace of its compact subsets $\mathcal{K}(E)$, we consider the class of $G_δ$ $σ$-ideals of compact subsets of $E$ that can be represented via a compact subset of $\mathcal{K}(E)$. If we extend such an ideal $I$ by considering $G_δ$ (or analytic) sets that are covered by countable unions of sets in $I$, we show that the extended collection can still be represented via some compact subset of $\mathcal{K}(E)$.

math.LO↗

arXiv2018

A note on $G_δ$ ideals of compact sets

Solecki has shown that a broad natural class of $G_δ$ ideals of compact sets can be represented through the ideal of nowhere dense subsets of a closed subset of the hyperspace of compact sets. In this note we show that the closed subset in this representation can be taken to be closed upwards.

math.LO↗