Geodesic
Separable Quotients of Free Topological Groups
Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 610-623

Voir la notice de l'article provenant de la source Cambridge University Press

We study the following problem: For which Tychonoff 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? The 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 $\unicode[STIX]{x1D70E}$-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.
DOI : 10.4153/S0008439519000699
Mots-clés : free topological group, quotient, separable 
Leiderman, Arkady; Tkachenko, Mikhail. Separable Quotients of Free Topological Groups. Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 610-623. doi: 10.4153/S0008439519000699
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