G_δ sets in σ-ideals generated by compact sets

2018/07/02 by Maya Saran, Saran, Maya
Computer Science · Mathematics · #03E15 #28A05 #54H05 #Advanced Algebra and Logic #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E15 #msc:28A05 #msc:54H05

paper · pdf · doi:10.48550/arxiv.1807.00845

New version (Feb 23, 2019) has corrected typos and minor changes to arguments. Results unchanged

openalex publication_date 2018/07/02 · openalex created_date 2018/07/10 · arxiv created 2019/02/23 · arxiv updated 2019/02/26 · openalex updated_date 2026/07/28

Abstract

Given a compact Polish space E and the hyperspace of its compact subsets 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 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 K(E).

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