$G_{\delta}$ sets in $\sigma$-ideals generated by compact sets

Maya Saran

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arXiv · 1807.00845

$G_{\delta}$ sets in $\sigma$-ideals generated by compact sets

Maya Saran

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Abstract

Given a compact Polish space $E$ and the hyperspace of its compact subsets $\mathcal{K}(E)$, we consider the class of $G_{\delta}$ $\sigma$-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 $G_{\delta}$ (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 $\mathcal{K}(E)$.

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BibTeX RIS

Maya Saran. 2018-07-02. $G_{\delta}$ sets in $\sigma$-ideals generated by compact sets. https://arxiv.org/abs/1807.00845

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