EMBEDDING OF THE FREE ABELIAN TOPOLOGICAL GROUP A(X⊕X) INTO A(X)

Mikołaj Krupski, Arkady Leiderman, Sidney Morris

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We consider the following question: for which metrizable separable spaces (Formula presented.) does the free abelian topological group (Formula presented.) isomorphically embed into (Formula presented.). While for many natural spaces (Formula presented.) such an embedding exists, our main result shows that if (Formula presented.) is a Cook continuum or (Formula presented.) is a rigid Bernstein set, then (Formula presented.) does not embed into (Formula presented.) as a topological subgroup. The analogous statement is true for the free boolean group (Formula presented.).

Original languageEnglish
Pages (from-to)708-718
Number of pages11
JournalMathematika
Volume65
Issue number3
DOIs
StatePublished - 1 Jan 2019

Keywords

  • 22A05
  • 54F15 (primary)

ASJC Scopus subject areas

  • General Mathematics

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