Gδ ideals of compact sets

Sławomir Solecki

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate the structure of Gδ ideals of compact sets. We define a class of Gδ ideals of compact sets that, on the one hand, avoids certain phenomena present among general Gδ ideals of compact sets and, on the other hand, includes all naturally occurring Gδ ideals of compact sets. We prove structural theorems for ideals in this class, and we describe how this class is placed among all G δ ideals. In particular, we establish a result representing ideals in this class via the meager ideal. This result is analogous to Choquet's theorem representing alternating capacities of order ∞via Borel probability measures. Methods coming from the structure theory of Banach spaces are used in constructing important examples of Gδ ideals outside of our class.

Original languageEnglish (US)
Pages (from-to)853-882
Number of pages30
JournalJournal of the European Mathematical Society
Volume13
Issue number4
DOIs
StatePublished - 2011

Keywords

  • Ideals of compact sets

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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