Separable quotients of free topological groups

Arkady Leiderman, Mikhail Tkachenko

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We study the following problem: For which Tychonoò spaces X do the free topological group F(X) and the free abelian topological group A(X) admit a quotient homomorphism onto a separable and nontrivial (i.e., not finitely generated) group? he existence of the required quotient homomorphisms is established for several important classes of spaces X, which include the class of pseudocompact spaces, the class of locally compact spaces, the class of σ-compact spaces, the class of connected locally connected spaces, and some others. We also show that there exists an infinite separable precompact topological abelian group G such that every quotient of G is either the one-point group or contains a dense non-separable subgroup and, hence, does not have a countable network.

Original languageEnglish
Pages (from-to)610-623
Number of pages14
JournalCanadian Mathematical Bulletin
Issue number3
StatePublished - 1 Sep 2020


  • Free topological group
  • Quotient
  • Separable

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Separable quotients of free topological groups'. Together they form a unique fingerprint.

Cite this