Separable Quotients of Free Topological Groups
Canadian mathematical bulletin, Tome 63 (2020) no. 3, pp. 610-623
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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.
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
@article{10_4153_S0008439519000699,
author = {Leiderman, Arkady and Tkachenko, Mikhail},
title = {Separable {Quotients} of {Free} {Topological} {Groups}},
journal = {Canadian mathematical bulletin},
pages = {610--623},
year = {2020},
volume = {63},
number = {3},
doi = {10.4153/S0008439519000699},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000699/}
}
TY - JOUR AU - Leiderman, Arkady AU - Tkachenko, Mikhail TI - Separable Quotients of Free Topological Groups JO - Canadian mathematical bulletin PY - 2020 SP - 610 EP - 623 VL - 63 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000699/ DO - 10.4153/S0008439519000699 ID - 10_4153_S0008439519000699 ER -
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