Local inverses of Borel homomorphisms and analytic P-ideals

Sławomir Solecki

Research output: Contribution to journalReview articlepeer-review

Abstract

We present a theorem on the existence of local continuous homomorphic inverses of surjective Borel homomorphisms with countable kernels from Borel groups onto Polish groups. We also associate in a canonical way subgroups of ℝ with certain analytic P-ideals of subsets of ℕ. These groups, with appropriate topologies, provide examples of Polish, nonlocally compact, totally disconnected groups for which global continuous homomorphic inverses exist in the situation described above. The method of producing these groups generalizes constructions of Stevens and Hjorth and, just as those constructions, yields examples of Polish groups which are totally disconnected and yet are generated by each neighborhood of the identity.

Original languageEnglish (US)
Pages (from-to)207-219
Number of pages13
JournalAbstract and Applied Analysis
Volume2005
Issue number3
DOIs
StatePublished - 2005

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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