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 language | English |
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Pages (from-to) | 708-718 |
Number of pages | 11 |
Journal | Mathematika |
Volume | 65 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jan 2019 |
Keywords
- 22A05
- 54F15 (primary)
ASJC Scopus subject areas
- General Mathematics